doc/proj.md
In Albluca/rpgraph: r interface to VDAOEngine to build elastic principal graphs
This document describes how to peoject points on a previously constructed principal graph.
Building a tree
This example will show how to project points on a principal tree. However, the procedure is completely generic and can be used with any principal graph.
library(rpgraph)
## Loading required package: rJava
##
## Attaching package: 'rpgraph'
## The following object is masked from 'package:base':
##
## Filter
Data <- simple_tree
Results <- computeElasticPrincipalGraph(Data = Data, NumNodes = 30, Method = 'DefaultPrincipalTreeConfiguration')
## Configuring engine ......[1] "Empty initialization"
## [1] ""
## [1] "Running engine"
By plotting the data in 2D we can see that different paths are present in the treee.
plotData2D(Data = simple_tree, PrintGraph = Results[[1]] ,
GroupsLab = rep(1, nrow(simple_circle)), Col = "black",
Main = "Pincipal tree",
Xlab = "Dimension 1", Ylab = "Dimension 2")
Making a network
To get the different paths we can use graph analysis approach supported by the igraph library. Firts of all, we need to construct a network from the princial graph.
library(igraph)
##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
Net <- ConstructGraph(Results = Results[[1]], DirectionMat = NULL)
We can now obtain the end points by looking at nodes with degree 1 and find the shorthest path between them.
EndPoints <- V(Net)[degree(Net) == 1]
AllPaths <- list()
for(StartIdx in 1:length(EndPoints)){
Paths <- get.shortest.paths(graph = Net, from = EndPoints[StartIdx], to = EndPoints[-StartIdx])
AllPaths <- append(AllPaths, Paths$vpath)
}
The paths found can be listed by looking at AllPaths.
AllPaths
## [[1]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_13 V_19 V_14 V_4 V_27 V_24 V_12 V_2
##
## [[2]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_26 V_28 V_17 V_6
##
## [[3]]
## + 13/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_13 V_19 V_14 V_4 V_27 V_24 V_15
##
## [[4]]
## + 13/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_20 V_30 V_7
##
## [[5]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_11 V_23 V_18 V_3
##
## [[6]]
## + 14/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[7]]
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26
## [15] V_28 V_17 V_6
##
## [[8]]
## + 4/30 vertices, named:
## [1] V_2 V_12 V_24 V_15
##
## [[9]]
## + 16/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_20
## [15] V_30 V_7
##
## [[10]]
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_11
## [15] V_23 V_18 V_3
##
## [[11]]
## + 14/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[12]]
## + 17/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_12 V_2
##
## [[13]]
## + 16/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_15
##
## [[14]]
## + 8/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_20 V_30 V_7
##
## [[15]]
## + 9/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_11 V_23 V_18 V_3
##
## [[16]]
## + 13/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[17]]
## + 4/30 vertices, named:
## [1] V_15 V_24 V_12 V_2
##
## [[18]]
## + 16/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26 V_28
## [15] V_17 V_6
##
## [[19]]
## + 15/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_20 V_30
## [15] V_7
##
## [[20]]
## + 16/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_11 V_23
## [15] V_18 V_3
##
## [[21]]
## + 13/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[22]]
## + 16/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27 V_24
## [15] V_12 V_2
##
## [[23]]
## + 8/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_26 V_28 V_17 V_6
##
## [[24]]
## + 15/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27 V_24
## [15] V_15
##
## [[25]]
## + 8/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_11 V_23 V_18 V_3
##
## [[26]]
## + 14/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[27]]
## + 17/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_12 V_2
##
## [[28]]
## + 9/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_26 V_28 V_17 V_6
##
## [[29]]
## + 16/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_15
##
## [[30]]
## + 8/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_20 V_30 V_7
We can also look at their lengh distribution
table(sapply(AllPaths, length))
##
## 4 8 9 13 14 15 16 17
## 2 4 2 4 6 2 6 4
barplot(table(sapply(AllPaths, length)), main = "Paths between the endpoints", xlab = "length", ylab = "Frequency")
For this example, we will select one of the longest paths.
SelPathIdx <- sample(which(sapply(AllPaths, length) == max(sapply(AllPaths, length))), 1)
SelPath <- AllPaths[[SelPathIdx]]
SelPath
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26
## [15] V_28 V_17 V_6
Projecting all the points
We can now project the points on the path
TaxonList <- getTaxonMap(Results = Results[[1]], Data = Data)
Projections <- projectPoints(Results = Results[[1]], Data = Data, TaxonList = TaxonList, UseR = TRUE)
Projections will now contains the projections of the points on the graph in the PointsOnEdgesCoords field. We can use this information to confirm that the points are correctly projected on the tree.
plot(Projections$PointsOnEdgesCoords[,1:2], xlab = "Dimension 1", ylab = "Dimension 2", main = "Point projections")
It is now possible to project the points on the selected path. Note that in the igraph representation of the principal graph the nodes have a "V_" prefix to their names that need to be removed when going back to the original point names which are defined by their names.
NumericPath <- as.numeric(unlist(lapply(strsplit(SelPath$name, "V_"), "[[", 2)))
It is now possible to order the points on the selected path. Note that points associated with edges not present in the path will not considered.
PathProjection <- OrderOnPath(PrinGraph = Results[[1]], Path = NumericPath, PointProjections = Projections)
## [1] "20 points found on edge"
## [1] "10 points found on edge"
## [1] "18 points found on edge"
## [1] "22 points found on edge"
## [1] "0 points found on edge"
## [1] "26 points found on edge"
## [1] "19 points found on edge"
## [1] "2 points found on edge"
## [1] "30 points found on edge"
## [1] "12 points found on edge"
## [1] "27 points found on edge"
## [1] "1 points found on edge"
## [1] "5 points found on edge"
## [1] "9 points found on edge"
## [1] "17 points found on edge"
## [1] "13 points found on edge"
The ordered points can now be plotted and color-coded according to their position (i.e. PathProjection$PositionOnPath).
plot(Projections$PointsOnEdgesCoords[order(PathProjection$PositionOnPath, na.last = NA),1:2], xlab = "Dimension 1", ylab = "Dimension 2", main = "Point projections", col=heat.colors(sum(!is.na(PathProjection$PositionOnPath))))
Albluca/rpgraph documentation built on May 5, 2019, 1:35 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
This document describes how to peoject points on a previously constructed principal graph.
Building a tree
This example will show how to project points on a principal tree. However, the procedure is completely generic and can be used with any principal graph.
library(rpgraph)
## Loading required package: rJava
##
## Attaching package: 'rpgraph'
## The following object is masked from 'package:base':
##
## Filter
Data <- simple_tree
Results <- computeElasticPrincipalGraph(Data = Data, NumNodes = 30, Method = 'DefaultPrincipalTreeConfiguration')
## Configuring engine ......[1] "Empty initialization"
## [1] ""
## [1] "Running engine"
By plotting the data in 2D we can see that different paths are present in the treee.
plotData2D(Data = simple_tree, PrintGraph = Results[[1]] ,
GroupsLab = rep(1, nrow(simple_circle)), Col = "black",
Main = "Pincipal tree",
Xlab = "Dimension 1", Ylab = "Dimension 2")
Making a network
To get the different paths we can use graph analysis approach supported by the igraph library. Firts of all, we need to construct a network from the princial graph.
library(igraph)
##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
Net <- ConstructGraph(Results = Results[[1]], DirectionMat = NULL)
We can now obtain the end points by looking at nodes with degree 1 and find the shorthest path between them.
EndPoints <- V(Net)[degree(Net) == 1]
AllPaths <- list()
for(StartIdx in 1:length(EndPoints)){
Paths <- get.shortest.paths(graph = Net, from = EndPoints[StartIdx], to = EndPoints[-StartIdx])
AllPaths <- append(AllPaths, Paths$vpath)
}
The paths found can be listed by looking at AllPaths.
AllPaths
## [[1]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_13 V_19 V_14 V_4 V_27 V_24 V_12 V_2
##
## [[2]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_26 V_28 V_17 V_6
##
## [[3]]
## + 13/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_13 V_19 V_14 V_4 V_27 V_24 V_15
##
## [[4]]
## + 13/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_20 V_30 V_7
##
## [[5]]
## + 14/30 vertices, named:
## [1] V_1 V_25 V_8 V_16 V_10 V_9 V_21 V_29 V_22 V_5 V_11 V_23 V_18 V_3
##
## [[6]]
## + 14/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[7]]
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26
## [15] V_28 V_17 V_6
##
## [[8]]
## + 4/30 vertices, named:
## [1] V_2 V_12 V_24 V_15
##
## [[9]]
## + 16/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_20
## [15] V_30 V_7
##
## [[10]]
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_11
## [15] V_23 V_18 V_3
##
## [[11]]
## + 14/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[12]]
## + 17/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_12 V_2
##
## [[13]]
## + 16/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_15
##
## [[14]]
## + 8/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_20 V_30 V_7
##
## [[15]]
## + 9/30 vertices, named:
## [1] V_6 V_17 V_28 V_26 V_5 V_11 V_23 V_18 V_3
##
## [[16]]
## + 13/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[17]]
## + 4/30 vertices, named:
## [1] V_15 V_24 V_12 V_2
##
## [[18]]
## + 16/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26 V_28
## [15] V_17 V_6
##
## [[19]]
## + 15/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_20 V_30
## [15] V_7
##
## [[20]]
## + 16/30 vertices, named:
## [1] V_15 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_11 V_23
## [15] V_18 V_3
##
## [[21]]
## + 13/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[22]]
## + 16/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27 V_24
## [15] V_12 V_2
##
## [[23]]
## + 8/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_26 V_28 V_17 V_6
##
## [[24]]
## + 15/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27 V_24
## [15] V_15
##
## [[25]]
## + 8/30 vertices, named:
## [1] V_7 V_30 V_20 V_5 V_11 V_23 V_18 V_3
##
## [[26]]
## + 14/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_10 V_16 V_8 V_25 V_1
##
## [[27]]
## + 17/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_12 V_2
##
## [[28]]
## + 9/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_26 V_28 V_17 V_6
##
## [[29]]
## + 16/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_22 V_29 V_21 V_9 V_13 V_19 V_14 V_4 V_27
## [15] V_24 V_15
##
## [[30]]
## + 8/30 vertices, named:
## [1] V_3 V_18 V_23 V_11 V_5 V_20 V_30 V_7
We can also look at their lengh distribution
table(sapply(AllPaths, length))
##
## 4 8 9 13 14 15 16 17
## 2 4 2 4 6 2 6 4
barplot(table(sapply(AllPaths, length)), main = "Paths between the endpoints", xlab = "length", ylab = "Frequency")
For this example, we will select one of the longest paths.
SelPathIdx <- sample(which(sapply(AllPaths, length) == max(sapply(AllPaths, length))), 1)
SelPath <- AllPaths[[SelPathIdx]]
SelPath
## + 17/30 vertices, named:
## [1] V_2 V_12 V_24 V_27 V_4 V_14 V_19 V_13 V_9 V_21 V_29 V_22 V_5 V_26
## [15] V_28 V_17 V_6
Projecting all the points
We can now project the points on the path
TaxonList <- getTaxonMap(Results = Results[[1]], Data = Data)
Projections <- projectPoints(Results = Results[[1]], Data = Data, TaxonList = TaxonList, UseR = TRUE)
Projections will now contains the projections of the points on the graph in the PointsOnEdgesCoords field. We can use this information to confirm that the points are correctly projected on the tree.
plot(Projections$PointsOnEdgesCoords[,1:2], xlab = "Dimension 1", ylab = "Dimension 2", main = "Point projections")
It is now possible to project the points on the selected path. Note that in the igraph representation of the principal graph the nodes have a "V_" prefix to their names that need to be removed when going back to the original point names which are defined by their names.
NumericPath <- as.numeric(unlist(lapply(strsplit(SelPath$name, "V_"), "[[", 2)))
It is now possible to order the points on the selected path. Note that points associated with edges not present in the path will not considered.
PathProjection <- OrderOnPath(PrinGraph = Results[[1]], Path = NumericPath, PointProjections = Projections)
## [1] "20 points found on edge"
## [1] "10 points found on edge"
## [1] "18 points found on edge"
## [1] "22 points found on edge"
## [1] "0 points found on edge"
## [1] "26 points found on edge"
## [1] "19 points found on edge"
## [1] "2 points found on edge"
## [1] "30 points found on edge"
## [1] "12 points found on edge"
## [1] "27 points found on edge"
## [1] "1 points found on edge"
## [1] "5 points found on edge"
## [1] "9 points found on edge"
## [1] "17 points found on edge"
## [1] "13 points found on edge"
The ordered points can now be plotted and color-coded according to their position (i.e. PathProjection$PositionOnPath).
plot(Projections$PointsOnEdgesCoords[order(PathProjection$PositionOnPath, na.last = NA),1:2], xlab = "Dimension 1", ylab = "Dimension 2", main = "Point projections", col=heat.colors(sum(!is.na(PathProjection$PositionOnPath))))
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