guides/base.md
In Albluca/ElPiGraph.R: Elastic principal graph construction
- Constructing a principal graph
- Examples of principal curves
- Using bootstrapping
- Plotting data with principal
graphs
Constructing a principal graph
The construction of a principal graph with a given topology is done via
the specification of an appropriate initial conditions and of
appropriate growth/shrink grammars. This can be done via the
computeElasticPrincipalGraph.
Specific wrapping functions are also provided to build commonly
encountered topologies (computeElasticPrincipalCurve,
`computeElasticPrincipalTree, computeElasticPrincipalCircle), with
minimal required inputs. In all of these function, it is necessary to
specify a numeric matrix with the data points (X) and the number of
nodes to of the principal graph (NumNodes). It is possible to control
the behavior of the algorithm via a set of optional parameters. For
example, it is possible to:
- modify the parameter controlling the elastic energy (
Mu and
Lambda)
- specify the number of processor to be used (
n.cores)
- indicate if diagnostic plots should be produced
(
drawAccuracyComplexity and drawEnergy)
- indicate if the final graph should be used to plotted non the data
(
drawPCAView)
- specify if PCA should be performed on the data prior to principal
graph fitting (
Do_PCA) and if dimensionality should be reduced
(ReduceDimension)
Examples of principal curves
The function computeElasticPrincipalCurve constructs a principal curve
on the data. For example to construct a principal curve with 50 nodes on
the example dataset line_data, it is sufficient to write
library("ElPiGraph.R")
CurveEPG <- computeElasticPrincipalCurve(X = curve_data, NumNodes = 60)
## [1] "Creating a chain in the 1st PC with 3 nodes"
## [1] "Constructing curve 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 60 nodes on 500 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||60 0.07975 60 59 58 0 0 0 0.04766 0.04544 0.9841 0.9849 0.02364 0.008445 0.5067 30.4 0
## 9.369 sec elapsed
## [[1]]
A principal tree can be constructed via the
computeElasticPrincipalTree function. For example to construct a
principal tree with 50 nodes on the example dataset tree_data, it is
sufficient to write
TreeEPG <- computeElasticPrincipalTree(X = tree_data, NumNodes = 60, Lambda = .03, Mu = .01)
## [1] "Creating a chain in the 1st PC with 2 nodes"
## [1] "Constructing tree 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 60 nodes on 492 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 1|2||60 0.01848 60 59 51 2 0 0 0.00548 0.005053 0.9898 0.9906 0.01249 0.0005134 0.03081 1.848 0
## 31.001 sec elapsed
## [[1]]
Finally, a principal circle can be constructed via the
computeElasticPrincipalCircle function. For example to construct a
principal circle with 50 nodes on the example dataset circe_data, it
is sufficient to write
CircleEPG <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 40)
## [1] "Using a single core"
## [1] "Creating a circle in the plane induced buy the 1st and 2nd PCs with 3 nodes"
## [1] "Constructing curve 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 200 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04107 40 40 40 0 0 0 0.02892 0.02738 0.9729 0.9744 0.0105 0.00165 0.066 2.64 0
## 1.807 sec elapsed
## [[1]]
All of these functions will return a list of length 1, with all the
information associated with the graph.
Using bootstrapping
All of the functions provided to build principal graphs allow a
bootstrapped construction. To enable that it is sufficient to modify the
parameters nReps and ProbPoint. nReps indicates the number of
repetitions and ProbPoint indicates the probability to include a point
in each of the repetition. When nReps is larger than 1, a final
consensus principal graph will be constructed using the nodes of the
graph derived in each repetition.
As an example, let us perform bootstrapping on the circle data. We will
also prevent the plotting, for now.
set.seed(42)
CircleEPG.Boot <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 40, nReps = 50, ProbPoint = .6,
drawAccuracyComplexity = FALSE, drawEnergy = FALSE, drawPCAView = FALSE)
## [1] "Using a single core"
## [1] "Creating a circle in the plane induced buy the 1st and 2nd PCs with 3 nodes"
## [1] "Constructing curve 1 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 108 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03681 40 40 40 0 0 0 0.02347 0.02213 0.9784 0.9796 0.01091 0.00244 0.09759 3.904 0
## 1.393 sec elapsed
## [1] "Constructing curve 2 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 137 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03783 40 40 40 0 0 0 0.02623 0.02488 0.975 0.9763 0.01009 0.001519 0.06075 2.43 0
## 1.675 sec elapsed
## [1] "Constructing curve 3 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 130 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03796 40 40 40 0 0 0 0.02512 0.0235 0.9766 0.9781 0.0107 0.002141 0.08564 3.426 0
## 1.283 sec elapsed
## [1] "Graphical output will be suppressed for the remaining replicas"
## [1] "Constructing curve 4 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03444 40 40 40 0 0 0 0.02167 0.02037 0.9791 0.9804 0.01067 0.002104 0.08415 3.366 0
## 1.306 sec elapsed
## [1] "Constructing curve 5 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 126 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03827 40 40 40 0 0 0 0.02623 0.02498 0.976 0.9771 0.01062 0.001419 0.05676 2.27 0
## 1.333 sec elapsed
## [1] "Constructing curve 6 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 125 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0383 40 40 40 0 0 0 0.02668 0.02533 0.9752 0.9764 0.01032 0.001298 0.05193 2.077 0
## 1.599 sec elapsed
## [1] "Constructing curve 7 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04172 40 40 40 0 0 0 0.02962 0.02814 0.9714 0.9728 0.01011 0.001993 0.0797 3.188 0
## 1.271 sec elapsed
## [1] "Constructing curve 8 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03527 40 40 40 0 0 0 0.02348 0.02223 0.9776 0.9788 0.01021 0.001579 0.06317 2.527 0
## 1.304 sec elapsed
## [1] "Constructing curve 9 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 125 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03911 40 40 40 0 0 0 0.02477 0.02332 0.9775 0.9788 0.01142 0.002913 0.1165 4.661 0
## 1.343 sec elapsed
## [1] "Constructing curve 10 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 103 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0391 40 40 40 0 0 0 0.02653 0.02537 0.9756 0.9767 0.01062 0.001941 0.07765 3.106 0
## 1.353 sec elapsed
## [1] "Constructing curve 11 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0404 40 40 40 0 0 0 0.02854 0.02731 0.9729 0.9741 0.01023 0.001625 0.06502 2.601 0
## 1.582 sec elapsed
## [1] "Constructing curve 12 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 109 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04414 40 40 40 0 0 0 0.0312 0.02985 0.971 0.9722 0.01062 0.002324 0.09295 3.718 0
## 1.277 sec elapsed
## [1] "Constructing curve 13 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 114 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04476 40 40 40 0 0 0 0.03171 0.03021 0.9713 0.9727 0.01095 0.002093 0.08374 3.349 0
## 1.315 sec elapsed
## [1] "Constructing curve 14 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03831 40 40 40 0 0 0 0.02639 0.02506 0.9749 0.9762 0.01036 0.001557 0.06229 2.492 0
## 1.338 sec elapsed
## [1] "Constructing curve 15 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 123 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03557 40 40 40 0 0 0 0.02417 0.02301 0.9772 0.9783 0.0102 0.001202 0.04808 1.923 0
## 1.357 sec elapsed
## [1] "Constructing curve 16 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 117 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04294 40 40 40 0 0 0 0.03028 0.02873 0.9721 0.9735 0.01053 0.00213 0.0852 3.408 0
## 1.577 sec elapsed
## [1] "Constructing curve 17 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03371 40 40 40 0 0 0 0.02143 0.02015 0.9801 0.9813 0.01049 0.001794 0.07174 2.87 0
## 1.289 sec elapsed
## [1] "Constructing curve 18 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03402 40 40 40 0 0 0 0.02173 0.02062 0.9794 0.9804 0.01038 0.001904 0.07617 3.047 0
## 1.324 sec elapsed
## [1] "Constructing curve 19 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03697 40 40 40 0 0 0 0.02527 0.02415 0.975 0.9761 0.01007 0.001628 0.06514 2.605 0
## 1.344 sec elapsed
## [1] "Constructing curve 20 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 120 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.041 40 40 40 0 0 0 0.02834 0.02711 0.9728 0.9739 0.01027 0.002388 0.09551 3.82 0
## 1.368 sec elapsed
## [1] "Constructing curve 21 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 112 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04118 40 40 40 0 0 0 0.02823 0.02703 0.9738 0.9749 0.01061 0.002333 0.09334 3.734 0
## 1.564 sec elapsed
## [1] "Constructing curve 22 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03874 40 40 40 0 0 0 0.0261 0.02452 0.976 0.9775 0.01069 0.001943 0.0777 3.108 0
## 1.321 sec elapsed
## [1] "Constructing curve 23 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03591 40 40 40 0 0 0 0.02385 0.02262 0.9777 0.9789 0.01034 0.001719 0.06878 2.751 0
## 1.316 sec elapsed
## [1] "Constructing curve 24 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 119 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04239 40 40 40 0 0 0 0.02992 0.02864 0.9724 0.9736 0.01041 0.002058 0.08231 3.292 0
## 1.367 sec elapsed
## [1] "Constructing curve 25 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04232 40 40 40 0 0 0 0.02937 0.02772 0.9737 0.9751 0.01087 0.002086 0.08345 3.338 0
## 1.376 sec elapsed
## [1] "Constructing curve 26 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04073 40 40 40 0 0 0 0.02844 0.02722 0.9727 0.9739 0.0102 0.002084 0.08337 3.335 0
## 1.531 sec elapsed
## [1] "Constructing curve 27 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0394 40 40 40 0 0 0 0.02529 0.02384 0.9768 0.9781 0.01141 0.002694 0.1078 4.31 0
## 1.304 sec elapsed
## [1] "Constructing curve 28 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 118 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04148 40 40 40 0 0 0 0.02713 0.02596 0.9748 0.9759 0.01099 0.003361 0.1344 5.378 0
## 1.347 sec elapsed
## [1] "Constructing curve 29 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04078 40 40 40 0 0 0 0.02767 0.02631 0.9749 0.9762 0.01094 0.00217 0.0868 3.472 0
## 1.364 sec elapsed
## [1] "Constructing curve 30 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 135 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04046 40 40 40 0 0 0 0.02848 0.02692 0.9732 0.9747 0.01024 0.001734 0.06934 2.774 0
## 1.634 sec elapsed
## [1] "Constructing curve 31 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 127 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04098 40 40 40 0 0 0 0.02817 0.02684 0.9745 0.9757 0.0109 0.001919 0.07676 3.07 0
## 1.293 sec elapsed
## [1] "Constructing curve 32 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03917 40 40 40 0 0 0 0.02744 0.02613 0.9734 0.9747 0.0101 0.001632 0.06527 2.611 0
## 1.319 sec elapsed
## [1] "Constructing curve 33 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03909 40 40 40 0 0 0 0.02651 0.02521 0.9748 0.9761 0.01046 0.002118 0.08473 3.389 0
## 1.35 sec elapsed
## [1] "Constructing curve 34 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 120 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03803 40 40 40 0 0 0 0.02536 0.02401 0.9766 0.9778 0.01062 0.002048 0.08194 3.277 0
## 1.371 sec elapsed
## [1] "Constructing curve 35 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 112 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03585 40 40 40 0 0 0 0.02297 0.02158 0.9789 0.9802 0.01085 0.002041 0.08166 3.266 0
## 1.589 sec elapsed
## [1] "Constructing curve 36 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 118 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04089 40 40 40 0 0 0 0.02808 0.02665 0.9741 0.9754 0.0108 0.002001 0.08004 3.202 0
## 1.3 sec elapsed
## [1] "Constructing curve 37 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 123 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04209 40 40 40 0 0 0 0.02984 0.02866 0.9716 0.9727 0.01039 0.001858 0.07434 2.974 0
## 1.333 sec elapsed
## [1] "Constructing curve 38 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04054 40 40 40 0 0 0 0.02796 0.02668 0.9734 0.9746 0.01028 0.002297 0.0919 3.676 0
## 1.348 sec elapsed
## [1] "Constructing curve 39 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 127 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04192 40 40 40 0 0 0 0.02814 0.02699 0.974 0.9751 0.011 0.002781 0.1112 4.45 0
## 1.387 sec elapsed
## [1] "Constructing curve 40 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04539 40 40 40 0 0 0 0.03227 0.03092 0.9705 0.9717 0.01064 0.002481 0.09922 3.969 0
## 1.573 sec elapsed
## [1] "Constructing curve 41 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 121 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03942 40 40 40 0 0 0 0.02747 0.02613 0.9749 0.9761 0.01052 0.001424 0.05694 2.278 0
## 1.305 sec elapsed
## [1] "Constructing curve 42 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 121 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04049 40 40 40 0 0 0 0.0277 0.02636 0.974 0.9753 0.01045 0.002337 0.09349 3.74 0
## 1.334 sec elapsed
## [1] "Constructing curve 43 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04184 40 40 40 0 0 0 0.02876 0.02747 0.9728 0.974 0.01057 0.00251 0.1004 4.017 0
## 1.363 sec elapsed
## [1] "Constructing curve 44 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0398 40 40 40 0 0 0 0.02691 0.02565 0.9755 0.9767 0.01078 0.002101 0.08402 3.361 0
## 1.633 sec elapsed
## [1] "Constructing curve 45 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04042 40 40 40 0 0 0 0.02774 0.02642 0.9745 0.9757 0.0107 0.001977 0.07909 3.164 0
## 1.29 sec elapsed
## [1] "Constructing curve 46 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 119 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03712 40 40 40 0 0 0 0.02346 0.02199 0.9781 0.9795 0.01092 0.002744 0.1098 4.391 0
## 1.327 sec elapsed
## [1] "Constructing curve 47 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03553 40 40 40 0 0 0 0.02395 0.02259 0.9774 0.9787 0.01032 0.001261 0.05043 2.017 0
## 1.363 sec elapsed
## [1] "Constructing curve 48 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 117 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03905 40 40 40 0 0 0 0.02643 0.02517 0.9754 0.9765 0.01047 0.002156 0.08625 3.45 0
## 1.378 sec elapsed
## [1] "Constructing curve 49 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03775 40 40 40 0 0 0 0.02614 0.02482 0.9749 0.9762 0.009958 0.001651 0.06604 2.642 0
## 1.594 sec elapsed
## [1] "Constructing curve 50 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 108 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03721 40 40 40 0 0 0 0.02558 0.02431 0.9762 0.9774 0.01022 0.001418 0.05673 2.269 0
## 1.302 sec elapsed
## [1] "Constructing average tree"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 2000 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.01414 40 40 40 0 0 0 0.003575 0.002329 0.9965 0.9977 0.009816 0.000747 0.02988 1.195 0
## 2.349 sec elapsed
CircleEPG.Boot will be a list with 51 elements: the 50 bootstrapped
circles and the final consensus one.
Plotting data with principal graphs
The ElPiGraph.R provides different functions to explore show how the
principal graph approximate the data. The main function is plotPG.
This function can be used to show how the principal graph fit the data
in different ways.
To plot the principal tree previously constructed we can type
PlotPG(X = tree_data, TargetPG = TreeEPG[[1]], Main = "A tree")
## [[1]]
The main plot reports different features including the percentage of
variance explained relative to the nodes of the principal graph (PG
var), the percentage of variance explained relative to the data points
(Data var), the fraction of variance of the data explained by the nodes
of the principal graph (FVE) and the fraction of variance of the data
explained by the projection of the points on the the principal graph
(FVEP). In this example the nodes of the principal graph have been used
to compute PCA and rotate the space (the Do_PCA parameter is TRUE be
default), this can be seen by the "EpG PC" label of the axes.
To include additional dimension in the plot it is sufficient to specify
them with the DimToPlot parameter, e.g.,
PlotPG(X = tree_data, TargetPG = TreeEPG[[1]], Main = "A tree", DimToPlot = 1:3)
## [[1]]
##
## [[2]]
##
## [[3]]
We can also visualize the results of the bootstrapped construction by
using the BootPG parameter:
PlotPG(X = circle_data, TargetPG = CircleEPG.Boot[[length(CircleEPG.Boot)]],
BootPG = CircleEPG.Boot[1:(length(CircleEPG.Boot)-1)],
Main = "A bootstrapped circle", DimToPlot = 1:2)
## [[1]]
Albluca/ElPiGraph.R documentation built on May 28, 2019, 11:02 a.m.
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- Constructing a principal graph
- Examples of principal curves
- Using bootstrapping
- Plotting data with principal graphs
Constructing a principal graph
The construction of a principal graph with a given topology is done via
the specification of an appropriate initial conditions and of
appropriate growth/shrink grammars. This can be done via the
computeElasticPrincipalGraph.
Specific wrapping functions are also provided to build commonly
encountered topologies (computeElasticPrincipalCurve,
`computeElasticPrincipalTree, computeElasticPrincipalCircle), with
minimal required inputs. In all of these function, it is necessary to
specify a numeric matrix with the data points (X) and the number of
nodes to of the principal graph (NumNodes). It is possible to control
the behavior of the algorithm via a set of optional parameters. For
example, it is possible to:
- modify the parameter controlling the elastic energy (
MuandLambda) - specify the number of processor to be used (
n.cores) - indicate if diagnostic plots should be produced
(
drawAccuracyComplexityanddrawEnergy) - indicate if the final graph should be used to plotted non the data
(
drawPCAView) - specify if PCA should be performed on the data prior to principal
graph fitting (
Do_PCA) and if dimensionality should be reduced (ReduceDimension)
Examples of principal curves
The function computeElasticPrincipalCurve constructs a principal curve
on the data. For example to construct a principal curve with 50 nodes on
the example dataset line_data, it is sufficient to write
library("ElPiGraph.R")
CurveEPG <- computeElasticPrincipalCurve(X = curve_data, NumNodes = 60)
## [1] "Creating a chain in the 1st PC with 3 nodes"
## [1] "Constructing curve 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 60 nodes on 500 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||60 0.07975 60 59 58 0 0 0 0.04766 0.04544 0.9841 0.9849 0.02364 0.008445 0.5067 30.4 0
## 9.369 sec elapsed
## [[1]]
A principal tree can be constructed via the
computeElasticPrincipalTree function. For example to construct a
principal tree with 50 nodes on the example dataset tree_data, it is
sufficient to write
TreeEPG <- computeElasticPrincipalTree(X = tree_data, NumNodes = 60, Lambda = .03, Mu = .01)
## [1] "Creating a chain in the 1st PC with 2 nodes"
## [1] "Constructing tree 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 60 nodes on 492 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 1|2||60 0.01848 60 59 51 2 0 0 0.00548 0.005053 0.9898 0.9906 0.01249 0.0005134 0.03081 1.848 0
## 31.001 sec elapsed
## [[1]]
Finally, a principal circle can be constructed via the
computeElasticPrincipalCircle function. For example to construct a
principal circle with 50 nodes on the example dataset circe_data, it
is sufficient to write
CircleEPG <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 40)
## [1] "Using a single core"
## [1] "Creating a circle in the plane induced buy the 1st and 2nd PCs with 3 nodes"
## [1] "Constructing curve 1 of 1 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 200 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04107 40 40 40 0 0 0 0.02892 0.02738 0.9729 0.9744 0.0105 0.00165 0.066 2.64 0
## 1.807 sec elapsed
## [[1]]
All of these functions will return a list of length 1, with all the information associated with the graph.
Using bootstrapping
All of the functions provided to build principal graphs allow a
bootstrapped construction. To enable that it is sufficient to modify the
parameters nReps and ProbPoint. nReps indicates the number of
repetitions and ProbPoint indicates the probability to include a point
in each of the repetition. When nReps is larger than 1, a final
consensus principal graph will be constructed using the nodes of the
graph derived in each repetition.
As an example, let us perform bootstrapping on the circle data. We will also prevent the plotting, for now.
set.seed(42)
CircleEPG.Boot <- computeElasticPrincipalCircle(X = circle_data, NumNodes = 40, nReps = 50, ProbPoint = .6,
drawAccuracyComplexity = FALSE, drawEnergy = FALSE, drawPCAView = FALSE)
## [1] "Using a single core"
## [1] "Creating a circle in the plane induced buy the 1st and 2nd PCs with 3 nodes"
## [1] "Constructing curve 1 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 108 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03681 40 40 40 0 0 0 0.02347 0.02213 0.9784 0.9796 0.01091 0.00244 0.09759 3.904 0
## 1.393 sec elapsed
## [1] "Constructing curve 2 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 137 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03783 40 40 40 0 0 0 0.02623 0.02488 0.975 0.9763 0.01009 0.001519 0.06075 2.43 0
## 1.675 sec elapsed
## [1] "Constructing curve 3 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 130 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03796 40 40 40 0 0 0 0.02512 0.0235 0.9766 0.9781 0.0107 0.002141 0.08564 3.426 0
## 1.283 sec elapsed
## [1] "Graphical output will be suppressed for the remaining replicas"
## [1] "Constructing curve 4 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03444 40 40 40 0 0 0 0.02167 0.02037 0.9791 0.9804 0.01067 0.002104 0.08415 3.366 0
## 1.306 sec elapsed
## [1] "Constructing curve 5 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 126 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03827 40 40 40 0 0 0 0.02623 0.02498 0.976 0.9771 0.01062 0.001419 0.05676 2.27 0
## 1.333 sec elapsed
## [1] "Constructing curve 6 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 125 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0383 40 40 40 0 0 0 0.02668 0.02533 0.9752 0.9764 0.01032 0.001298 0.05193 2.077 0
## 1.599 sec elapsed
## [1] "Constructing curve 7 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04172 40 40 40 0 0 0 0.02962 0.02814 0.9714 0.9728 0.01011 0.001993 0.0797 3.188 0
## 1.271 sec elapsed
## [1] "Constructing curve 8 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03527 40 40 40 0 0 0 0.02348 0.02223 0.9776 0.9788 0.01021 0.001579 0.06317 2.527 0
## 1.304 sec elapsed
## [1] "Constructing curve 9 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 125 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03911 40 40 40 0 0 0 0.02477 0.02332 0.9775 0.9788 0.01142 0.002913 0.1165 4.661 0
## 1.343 sec elapsed
## [1] "Constructing curve 10 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 103 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0391 40 40 40 0 0 0 0.02653 0.02537 0.9756 0.9767 0.01062 0.001941 0.07765 3.106 0
## 1.353 sec elapsed
## [1] "Constructing curve 11 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0404 40 40 40 0 0 0 0.02854 0.02731 0.9729 0.9741 0.01023 0.001625 0.06502 2.601 0
## 1.582 sec elapsed
## [1] "Constructing curve 12 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 109 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04414 40 40 40 0 0 0 0.0312 0.02985 0.971 0.9722 0.01062 0.002324 0.09295 3.718 0
## 1.277 sec elapsed
## [1] "Constructing curve 13 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 114 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04476 40 40 40 0 0 0 0.03171 0.03021 0.9713 0.9727 0.01095 0.002093 0.08374 3.349 0
## 1.315 sec elapsed
## [1] "Constructing curve 14 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03831 40 40 40 0 0 0 0.02639 0.02506 0.9749 0.9762 0.01036 0.001557 0.06229 2.492 0
## 1.338 sec elapsed
## [1] "Constructing curve 15 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 123 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03557 40 40 40 0 0 0 0.02417 0.02301 0.9772 0.9783 0.0102 0.001202 0.04808 1.923 0
## 1.357 sec elapsed
## [1] "Constructing curve 16 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 117 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04294 40 40 40 0 0 0 0.03028 0.02873 0.9721 0.9735 0.01053 0.00213 0.0852 3.408 0
## 1.577 sec elapsed
## [1] "Constructing curve 17 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03371 40 40 40 0 0 0 0.02143 0.02015 0.9801 0.9813 0.01049 0.001794 0.07174 2.87 0
## 1.289 sec elapsed
## [1] "Constructing curve 18 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03402 40 40 40 0 0 0 0.02173 0.02062 0.9794 0.9804 0.01038 0.001904 0.07617 3.047 0
## 1.324 sec elapsed
## [1] "Constructing curve 19 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03697 40 40 40 0 0 0 0.02527 0.02415 0.975 0.9761 0.01007 0.001628 0.06514 2.605 0
## 1.344 sec elapsed
## [1] "Constructing curve 20 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 120 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.041 40 40 40 0 0 0 0.02834 0.02711 0.9728 0.9739 0.01027 0.002388 0.09551 3.82 0
## 1.368 sec elapsed
## [1] "Constructing curve 21 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 112 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04118 40 40 40 0 0 0 0.02823 0.02703 0.9738 0.9749 0.01061 0.002333 0.09334 3.734 0
## 1.564 sec elapsed
## [1] "Constructing curve 22 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03874 40 40 40 0 0 0 0.0261 0.02452 0.976 0.9775 0.01069 0.001943 0.0777 3.108 0
## 1.321 sec elapsed
## [1] "Constructing curve 23 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03591 40 40 40 0 0 0 0.02385 0.02262 0.9777 0.9789 0.01034 0.001719 0.06878 2.751 0
## 1.316 sec elapsed
## [1] "Constructing curve 24 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 119 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04239 40 40 40 0 0 0 0.02992 0.02864 0.9724 0.9736 0.01041 0.002058 0.08231 3.292 0
## 1.367 sec elapsed
## [1] "Constructing curve 25 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 115 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04232 40 40 40 0 0 0 0.02937 0.02772 0.9737 0.9751 0.01087 0.002086 0.08345 3.338 0
## 1.376 sec elapsed
## [1] "Constructing curve 26 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04073 40 40 40 0 0 0 0.02844 0.02722 0.9727 0.9739 0.0102 0.002084 0.08337 3.335 0
## 1.531 sec elapsed
## [1] "Constructing curve 27 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0394 40 40 40 0 0 0 0.02529 0.02384 0.9768 0.9781 0.01141 0.002694 0.1078 4.31 0
## 1.304 sec elapsed
## [1] "Constructing curve 28 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 118 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04148 40 40 40 0 0 0 0.02713 0.02596 0.9748 0.9759 0.01099 0.003361 0.1344 5.378 0
## 1.347 sec elapsed
## [1] "Constructing curve 29 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04078 40 40 40 0 0 0 0.02767 0.02631 0.9749 0.9762 0.01094 0.00217 0.0868 3.472 0
## 1.364 sec elapsed
## [1] "Constructing curve 30 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 135 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04046 40 40 40 0 0 0 0.02848 0.02692 0.9732 0.9747 0.01024 0.001734 0.06934 2.774 0
## 1.634 sec elapsed
## [1] "Constructing curve 31 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 127 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04098 40 40 40 0 0 0 0.02817 0.02684 0.9745 0.9757 0.0109 0.001919 0.07676 3.07 0
## 1.293 sec elapsed
## [1] "Constructing curve 32 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03917 40 40 40 0 0 0 0.02744 0.02613 0.9734 0.9747 0.0101 0.001632 0.06527 2.611 0
## 1.319 sec elapsed
## [1] "Constructing curve 33 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03909 40 40 40 0 0 0 0.02651 0.02521 0.9748 0.9761 0.01046 0.002118 0.08473 3.389 0
## 1.35 sec elapsed
## [1] "Constructing curve 34 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 120 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03803 40 40 40 0 0 0 0.02536 0.02401 0.9766 0.9778 0.01062 0.002048 0.08194 3.277 0
## 1.371 sec elapsed
## [1] "Constructing curve 35 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 112 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03585 40 40 40 0 0 0 0.02297 0.02158 0.9789 0.9802 0.01085 0.002041 0.08166 3.266 0
## 1.589 sec elapsed
## [1] "Constructing curve 36 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 118 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04089 40 40 40 0 0 0 0.02808 0.02665 0.9741 0.9754 0.0108 0.002001 0.08004 3.202 0
## 1.3 sec elapsed
## [1] "Constructing curve 37 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 123 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04209 40 40 40 0 0 0 0.02984 0.02866 0.9716 0.9727 0.01039 0.001858 0.07434 2.974 0
## 1.333 sec elapsed
## [1] "Constructing curve 38 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04054 40 40 40 0 0 0 0.02796 0.02668 0.9734 0.9746 0.01028 0.002297 0.0919 3.676 0
## 1.348 sec elapsed
## [1] "Constructing curve 39 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 127 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04192 40 40 40 0 0 0 0.02814 0.02699 0.974 0.9751 0.011 0.002781 0.1112 4.45 0
## 1.387 sec elapsed
## [1] "Constructing curve 40 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04539 40 40 40 0 0 0 0.03227 0.03092 0.9705 0.9717 0.01064 0.002481 0.09922 3.969 0
## 1.573 sec elapsed
## [1] "Constructing curve 41 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 121 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03942 40 40 40 0 0 0 0.02747 0.02613 0.9749 0.9761 0.01052 0.001424 0.05694 2.278 0
## 1.305 sec elapsed
## [1] "Constructing curve 42 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 121 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04049 40 40 40 0 0 0 0.0277 0.02636 0.974 0.9753 0.01045 0.002337 0.09349 3.74 0
## 1.334 sec elapsed
## [1] "Constructing curve 43 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 116 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04184 40 40 40 0 0 0 0.02876 0.02747 0.9728 0.974 0.01057 0.00251 0.1004 4.017 0
## 1.363 sec elapsed
## [1] "Constructing curve 44 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.0398 40 40 40 0 0 0 0.02691 0.02565 0.9755 0.9767 0.01078 0.002101 0.08402 3.361 0
## 1.633 sec elapsed
## [1] "Constructing curve 45 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 122 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.04042 40 40 40 0 0 0 0.02774 0.02642 0.9745 0.9757 0.0107 0.001977 0.07909 3.164 0
## 1.29 sec elapsed
## [1] "Constructing curve 46 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 119 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03712 40 40 40 0 0 0 0.02346 0.02199 0.9781 0.9795 0.01092 0.002744 0.1098 4.391 0
## 1.327 sec elapsed
## [1] "Constructing curve 47 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 113 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03553 40 40 40 0 0 0 0.02395 0.02259 0.9774 0.9787 0.01032 0.001261 0.05043 2.017 0
## 1.363 sec elapsed
## [1] "Constructing curve 48 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 117 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03905 40 40 40 0 0 0 0.02643 0.02517 0.9754 0.9765 0.01047 0.002156 0.08625 3.45 0
## 1.378 sec elapsed
## [1] "Constructing curve 49 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 124 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03775 40 40 40 0 0 0 0.02614 0.02482 0.9749 0.9762 0.009958 0.001651 0.06604 2.642 0
## 1.594 sec elapsed
## [1] "Constructing curve 50 of 50 / Subset 1 of 1"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 108 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.03721 40 40 40 0 0 0 0.02558 0.02431 0.9762 0.9774 0.01022 0.001418 0.05673 2.269 0
## 1.302 sec elapsed
## [1] "Constructing average tree"
## [1] "Performing PCA on the data"
## [1] "Using standard PCA"
## [1] "3 dimensions are being used"
## [1] "100% of the original variance has been retained"
## [1] "Computing EPG with 40 nodes on 2000 points and 3 dimensions"
## [1] "Using a single core"
## Nodes = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
## BARCODE ENERGY NNODES NEDGES NRIBS NSTARS NRAYS NRAYS2 MSE MSEP FVE FVEP UE UR URN URN2 URSD
## 0||40 0.01414 40 40 40 0 0 0 0.003575 0.002329 0.9965 0.9977 0.009816 0.000747 0.02988 1.195 0
## 2.349 sec elapsed
CircleEPG.Boot will be a list with 51 elements: the 50 bootstrapped
circles and the final consensus one.
Plotting data with principal graphs
The ElPiGraph.R provides different functions to explore show how the
principal graph approximate the data. The main function is plotPG.
This function can be used to show how the principal graph fit the data
in different ways.
To plot the principal tree previously constructed we can type
PlotPG(X = tree_data, TargetPG = TreeEPG[[1]], Main = "A tree")
## [[1]]
The main plot reports different features including the percentage of variance explained relative to the nodes of the principal graph (PG var), the percentage of variance explained relative to the data points (Data var), the fraction of variance of the data explained by the nodes of the principal graph (FVE) and the fraction of variance of the data explained by the projection of the points on the the principal graph (FVEP). In this example the nodes of the principal graph have been used to compute PCA and rotate the space (the Do_PCA parameter is TRUE be default), this can be seen by the "EpG PC" label of the axes.
To include additional dimension in the plot it is sufficient to specify them with the DimToPlot parameter, e.g.,
PlotPG(X = tree_data, TargetPG = TreeEPG[[1]], Main = "A tree", DimToPlot = 1:3)
## [[1]]
##
## [[2]]
##
## [[3]]
We can also visualize the results of the bootstrapped construction by
using the BootPG parameter:
PlotPG(X = circle_data, TargetPG = CircleEPG.Boot[[length(CircleEPG.Boot)]],
BootPG = CircleEPG.Boot[1:(length(CircleEPG.Boot)-1)],
Main = "A bootstrapped circle", DimToPlot = 1:2)
## [[1]]
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