mine: MINE family statistics Maximal Information-Based...
In minerva: Maximal Information-Based Nonparametric Exploration for Variable Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
MINE family statistics
Maximal Information-Based Nonparametric Exploration (MINE)
statistics. mine computes the MINE family measures between two variables.
Usage
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Arguments
x
a numeric vector (of size n), matrix or data frame (which is coerced to matrix).
y
NULL (default) or a numeric vector of size n (i.e., with compatible dimensions to x).
master
an optional vector of indices (numeric or character) to
be given when y is not set, otherwise master is ignored. It can be
either one column index to be used as reference for the comparison
(versus all other columns) or a vector of column indices to be used for
computing all mutual statistics.
alpha
float (0, 1.0] or >=4 if alpha is in (0,1] then B will be max(n^alpha, 4) where n is the
number of samples. If alpha is >=4 then alpha defines directly the B
parameter. If alpha is higher than the number of samples (n) it will be
limited to be n, so B = min(alpha, n) Default value is 0.6 (see Details).
C
an optional number determining the starting point of the
X-by-Y search-grid. When trying to partition the x-axis into
X columns, the algorithm will start with at most CX
clumps. Default value is 15 (see Details).
n.cores
ooptional number of cores to be used in the
computations, when master is specified. It requires the
parallel package, which provides support for parallel
computing, released with R >= 2.14.0. Defaults is 1 (i.e., not performing parallel computing).
var.thr
minimum value allowed for the variance of the input
variables, since mine can not be computed in case of variance
close to 0. Default value is 1e-5. Information about failed check
are reported in var_thr.log file.
eps
integer in [0,1]. If 'NULL' (default) it is set to
1-MIC. It can be set to zero for noiseless functions,
but the default choice is the most appropriate parametrization
for general cases (as stated in Reshef et al. SOM).
It provides robustness.
est
Default value is "mic_approx". With est="mic_approx" the original MINE statistics will
be computed, with est="mic_e" the equicharacteristic matrix is
is evaluated and the mic() and tic() methods will return MIC_e and
TIC_e values respectively.
na.rm
boolean. This variable is passed directly to the
cor-based functions. See cor for further details.
use
Default value is "all.obs". This variable is passed directly to the
cor-based functions. See cor for further details.
normalization
logical whether to use normalization when computing tic measure. Ignored for other measures.
Default to FALSE.
...
currently ignored
Details
mine is an R wrapper for the C engine cmine
(http://minepy.readthedocs.io/en/latest/),
an implementation of Maximal Information-Based Nonparametric Exploration (MINE)
statistics. The MINE statistics were firstly detailed in
D. Reshef et al. (2011) Detecting novel associations in large datasets.
Science 334, 6062 (http://www.exploredata.net).
Here we recall the main concepts of the MINE family statistics.
Let D={(x,y)} be the set of n ordered pairs of elements of x
and y. The data space is partitioned in
an X-by-Y grid, grouping the x and y values
in X and Y bins respectively.
The Maximal Information Coefficient (MIC) is defined as
MIC(D)=max_{XY<B(n)} M(D)_{X,Y}=max_{XY<B(n)} I*(D,X,Y)/log(min(X,Y)),
where
B(n)=n^{α} is the search-grid size,
I*(D,X,Y)
is the maximum mutual information over all grids X-by-Y, of the distribution induced by D on
a grid having X and Y bins (where the probability mass on a cell
of the grid is the fraction of points of D falling in that cell).
The other statistics of the MINE family are derived from the mutual information
matrix achieved by an X-by-Y grid on D.
The Maximum Asymmetry Score (MAS) is defined as
MAS(D) = max_{XY<B(n)} |M(D)_{X,Y} - M(D)_{Y,X}|.
The Maximum Edge Value (MEV) is defined as
MEV(D) = max_{XY<B(n)} {M(D)_{X,Y}: X=2 or Y=2}.
The Minimum Cell Number (MCN) is defined as
MCN(D,ε) = min_{XY<B(n)} {log(XY): M(D)_{X,Y} >= (1-ε)MIC(D)}.
More details are provided in the supplementary material (SOM) of the original paper.
The MINE statistics can be computed for two numeric vectors x and y.
Otherwise a matrix (or data frame) can be provided and two options are available
according to the value of master. If master is a column identifier,
then the MINE statistics are computed for the master variable versus the
other matrix columns. If master is a set of column identifiers, then all
mutual MINE statistics are computed among the column subset.
master, alpha, and C refers respectively to the style,
exp, and c parameters of the original java code.
In the original article, the authors state that the default value α=0.6
(which is the exponent of the search-grid size B(n)=n^{α}) has been
empirically chosen. It is worthwhile noting that alpha and C are
defined to obtain an heuristic approximation in a reasonable amount of time. In case
of small sample size (n) it is preferable to increase alpha to 1 to
obtain a solution closer to the theoretical one.
Value
The Maximal Information-Based Nonparametric Exploration (MINE) statistics
provide quantitative evaluations of different aspects of the relationship
between two variables.
In particular mine returns a list of 5 statistics:
MIC
Maximal Information Coefficient.
It is related to the relationship strenght and it can be interpreted as a
correlation measure. It is symmetric and it ranges in [0,1], where it
tends to 0 for statistically independent data and it approaches 1 in
probability for noiseless functional relationships (more details can
ben found in the original paper).
MAS
Maximum Asymmetry Score.
It captures the deviation from monotonicity. Note that
MAS < MIC.
Note: it can be useful for detecting periodic relationships
(unknown frequencies).
MEV
Maximum Edge Value.
It measures the closeness to being a function. Note that
MEV <= MIC.
MCN
Minimum Cell Number.
It is a complexity measure.
MIC-R2
It is the difference between the MIC value and the Pearson
correlation coefficient.
When computing mine between two numeric vectors x and y,
the output is a list of 5 numeric values. When master is provided,
mine returns a list of 5 matrices having ncol equal to
m. In particular, if master is a single value,
then mine returns a list of 5 matrices having 1 column,
whose rows correspond to the MINE measures between the master
column versus all. Instead if master is a vector of m indices,
then mine output is a list of 5 m-by-m matrices, whose element
i,j corresponds to the MINE statistics computed between the i
and j columns of x.
Author(s)
Michele Filosi and Roberto Visintainer
References
D. Reshef, Y. Reshef, H. Finucane, S. Grossman, G. McVean, P. Turnbaugh,
E. Lander, M. Mitzenmacher, P. Sabeti. (2011)
Detecting novel associations in large datasets.
Science 334, 6062
http://www.exploredata.net
(SOM: Supplementary Online Material at
https://science.sciencemag.org/content/suppl/2011/12/14/334.6062.1518.DC1)
D. Albanese, M. Filosi, R. Visintainer, S. Riccadonna, G. Jurman,
C. Furlanello.
minerva and minepy: a C engine for the MINE suite and its R, Python and MATLAB wrappers.
Bioinformatics (2013) 29(3): 407-408, doi: 10.1093/bioinformatics/bts707.
minepy. Maximal Information-based Nonparametric Exploration in C and Python.
http://minepy.sourceforge.net
Examples
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A <- matrix(runif(50),nrow=5)
mine(x=A, master=1)
mine(x=A, master=c(1,3,5,7,8:10))
x <- runif(10); y <- 3*x+2; plot(x,y,type="l")
mine(x,y)
# MIC = 1
# MAS = 0
# MEV = 1
# MCN = 2
# MIC-R2 = 0
set.seed(100); x <- runif(10); y <- 3*x+2+rnorm(10,mean=2,sd=5); plot(x,y)
mine(x,y)
# rounded values of MINE statistics
# MIC = 0.61
# MAS = 0
# MEV = 0.61
# MCN = 2
# MIC-R2 = 0.13
t <-seq(-2*pi,2*pi,0.2); y1 <- sin(2*t); plot(t,y1,type="l")
mine(t,y1)
# rounded values of MINE statistics
# MIC = 0.66
# MAS = 0.37
# MEV = 0.66
# MCN = 3.58
# MIC-R2 = 0.62
y2 <- sin(4*t); plot(t,y2,type="l")
mine(t,y2)
# rounded values of MINE statistics
# MIC = 0.32
# MAS = 0.18
# MEV = 0.32
# MCN = 3.58
# MIC-R2 = 0.31
# Note that for small n it is better to increase alpha
mine(t,y1,alpha=1)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.59
# MEV = 1
# MCN = 5.67
# MIC-R2 = 0.96
mine(t,y2,alpha=1)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.59
# MEV = 1
# MCN = 5
# MIC-R2 = 0.99
# Some examples from SOM
x <- runif(n=1000, min=0, max=1)
# Linear relationship
y1 <- x; plot(x,y1,type="l"); mine(x,y1)
# MIC = 1
# MAS = 0
# MEV = 1
# MCN = 4
# MIC-R2 = 0
# Parabolic relationship
y2 <- 4*(x-0.5)^2; plot(sort(x),y2[order(x)],type="l"); mine(x,y2)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.68
# MEV = 1
# MCN = 5.5
# MIC-R2 = 1
# Sinusoidal relationship (varying frequency)
y3 <- sin(6*pi*x*(1+x)); plot(sort(x),y3[order(x)],type="l"); mine(x,y3)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.85
# MEV = 1
# MCN = 4.6
# MIC-R2 = 0.96
# Circle relationship
t <- seq(from=0,to=2*pi,length.out=1000)
x4 <- cos(t); y4 <- sin(t); plot(x4, y4, type="l",asp=1)
mine(x4,y4)
# rounded values of MINE statistics
# MIC = 0.68
# MAS = 0.01
# MEV = 0.32
# MCN = 5.98
# MIC-R2 = 0.68
data(Spellman)
res <- mine(Spellman,master=1,n.cores=1)
## Not run: ## example of multicore computation
res <- mine(Spellman,master=1,n.cores=parallel::detectCores()-1)
## End(Not run)
Example output
$MIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MAS
[,1]
[1,] 0
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 0
[8,] 0
[9,] 0
[10,] 0
$MEV
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MCN
[,1]
[1,] 2
[2,] 2
[3,] 2
[4,] 2
[5,] 2
[6,] 2
[7,] 2
[8,] 2
[9,] 2
[10,] 2
$MICR2
[,1]
[1,] -0.02904941
[2,] 0.31966063
[3,] 0.09011389
[4,] 0.26547216
[5,] 0.18254976
[6,] 0.14696220
[7,] 0.65189905
[8,] 0.21821985
[9,] 0.41456301
[10,] 0.62088731
$GMIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$TIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MAS
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0 0 0 0 0 0 0
[2,] 0 0 0 0 0 0 0
[3,] 0 0 0 0 0 0 0
[4,] 0 0 0 0 0 0 0
[5,] 0 0 0 0 0 0 0
[6,] 0 0 0 0 0 0 0
[7,] 0 0 0 0 0 0 0
$MEV
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MCN
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 2 2 2 2 2 2 2
[2,] 2 2 2 2 2 2 2
[3,] 2 2 2 2 2 2 2
[4,] 2 2 2 2 2 2 2
[5,] 2 2 2 2 2 2 2
[6,] 2 2 2 2 2 2 2
[7,] 2 2 2 2 2 2 2
$MICR2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.02904941 0.09011389 0.18254976 0.65189905 0.21821985 0.41456301
[2,] 0.09011389 -0.02904941 -0.09180528 0.15745852 0.13864789 0.41172109
[3,] 0.18254976 -0.09180528 -0.02904941 0.39742169 0.10641182 0.05299923
[4,] 0.65189905 0.15745852 0.39742169 -0.02904941 0.34883796 0.26908462
[5,] 0.21821985 0.13864789 0.10641182 0.34883796 -0.02904941 0.23458887
[6,] 0.41456301 0.41172109 0.05299923 0.26908462 0.23458887 -0.02904941
[7,] 0.62088731 0.03484033 0.39962969 0.24080761 0.28604760 -0.02912810
[,7]
[1,] 0.62088731
[2,] 0.03484033
[3,] 0.39962969
[4,] 0.24080761
[5,] 0.28604760
[6,] -0.02912810
[7,] -0.02904941
$GMIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$TIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MIC
[1] 1
$MAS
[1] 0
$MEV
[1] 1
$MCN
[1] 2
$`MIC-R2`
[1] 4.440892e-16
$GMIC
[1] 1
$TIC
[1] 1
$MIC
[1] 0.6099865
$MAS
[1] 0
$MEV
[1] 0.6099865
$MCN
[1] 2
$`MIC-R2`
[1] 0.1292083
$GMIC
[1] 0.6099865
$TIC
[1] 0.6099865
$MIC
[1] 0.6595235
$MAS
[1] 0.3737366
$MEV
[1] 0.6595235
$MCN
[1] 3.321928
$`MIC-R2`
[1] 0.6224055
$GMIC
[1] 0.3662762
$TIC
[1] 3.239177
$MIC
[1] 0.3239506
$MAS
[1] 0.1797499
$MEV
[1] 0.3239506
$MCN
[1] 2.584963
$`MIC-R2`
[1] 0.3151076
$GMIC
[1] 0.1819568
$TIC
[1] 1.852355
$MIC
[1] 1
$MAS
[1] 0.5869921
$MEV
[1] 0.9998182
$MCN
[1] 5.672425
$`MIC-R2`
[1] 0.962882
$GMIC
[1] 0.8704609
$TIC
[1] 84.0454
$MIC
[1] 0.9998182
$MAS
[1] 0.5914029
$MEV
[1] 0.9998182
$MCN
[1] 5
$`MIC-R2`
[1] 0.9909753
$GMIC
[1] 0.6522253
$TIC
[1] 70.02181
$MIC
[1] 1
$MAS
[1] 0
$MEV
[1] 1
$MCN
[1] 2
$`MIC-R2`
[1] 2.664535e-15
$GMIC
[1] 1
$TIC
[1] 147.9999
$MIC
[1] 1
$MAS
[1] 0.6460554
$MEV
[1] 1
$MCN
[1] 2.584963
$`MIC-R2`
[1] 0.9967731
$GMIC
[1] 0.9878122
$TIC
[1] 110.6488
$MIC
[1] 1
$MAS
[1] 0.8636941
$MEV
[1] 1
$MCN
[1] 4.70044
$`MIC-R2`
[1] 0.9582387
$GMIC
[1] 0.8121197
$TIC
[1] 56.29453
$MIC
[1] 0.6829015
$MAS
[1] 0.01067816
$MEV
[1] 0.3219625
$MCN
[1] 3.169925
$`MIC-R2`
[1] 0.6829015
$GMIC
[1] 0.03442878
$TIC
[1] 73.03107
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Description Usage Arguments Details Value Author(s) References Examples
Description
MINE family statistics
Maximal Information-Based Nonparametric Exploration (MINE)
statistics. mine computes the MINE family measures between two variables.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
Arguments
x |
a numeric vector (of size n), matrix or data frame (which is coerced to matrix). |
y |
NULL (default) or a numeric vector of size n (i.e., with compatible dimensions to x). |
master |
an optional vector of indices (numeric or character) to
be given when |
alpha |
float (0, 1.0] or >=4 if alpha is in (0,1] then B will be max(n^alpha, 4) where n is the number of samples. If alpha is >=4 then alpha defines directly the B parameter. If alpha is higher than the number of samples (n) it will be limited to be n, so B = min(alpha, n) Default value is 0.6 (see Details). |
C |
an optional number determining the starting point of the
X-by-Y search-grid. When trying to partition the x-axis into
X columns, the algorithm will start with at most |
n.cores |
ooptional number of cores to be used in the computations, when master is specified. It requires the parallel package, which provides support for parallel computing, released with R >= 2.14.0. Defaults is 1 (i.e., not performing parallel computing). |
var.thr |
minimum value allowed for the variance of the input
variables, since |
eps |
integer in [0,1]. If 'NULL' (default) it is set to 1-MIC. It can be set to zero for noiseless functions, but the default choice is the most appropriate parametrization for general cases (as stated in Reshef et al. SOM). It provides robustness. |
est |
Default value is "mic_approx". With est="mic_approx" the original MINE statistics will be computed, with est="mic_e" the equicharacteristic matrix is is evaluated and the mic() and tic() methods will return MIC_e and TIC_e values respectively. |
na.rm |
boolean. This variable is passed directly to the
|
use |
Default value is "all.obs". This variable is passed directly to the
|
normalization |
logical whether to use normalization when computing |
... |
currently ignored |
Details
mine is an R wrapper for the C engine cmine
(http://minepy.readthedocs.io/en/latest/),
an implementation of Maximal Information-Based Nonparametric Exploration (MINE)
statistics. The MINE statistics were firstly detailed in
D. Reshef et al. (2011) Detecting novel associations in large datasets.
Science 334, 6062 (http://www.exploredata.net).
Here we recall the main concepts of the MINE family statistics.
Let D={(x,y)} be the set of n ordered pairs of elements of x
and y. The data space is partitioned in
an X-by-Y grid, grouping the x and y values
in X and Y bins respectively.
The Maximal Information Coefficient (MIC) is defined as
MIC(D)=max_{XY<B(n)} M(D)_{X,Y}=max_{XY<B(n)} I*(D,X,Y)/log(min(X,Y)),
where
B(n)=n^{α} is the search-grid size,
I*(D,X,Y)
is the maximum mutual information over all grids X-by-Y, of the distribution induced by D on
a grid having X and Y bins (where the probability mass on a cell
of the grid is the fraction of points of D falling in that cell).
The other statistics of the MINE family are derived from the mutual information
matrix achieved by an X-by-Y grid on D.
The Maximum Asymmetry Score (MAS) is defined as
MAS(D) = max_{XY<B(n)} |M(D)_{X,Y} - M(D)_{Y,X}|.
The Maximum Edge Value (MEV) is defined as
MEV(D) = max_{XY<B(n)} {M(D)_{X,Y}: X=2 or Y=2}.
The Minimum Cell Number (MCN) is defined as
MCN(D,ε) = min_{XY<B(n)} {log(XY): M(D)_{X,Y} >= (1-ε)MIC(D)}.
More details are provided in the supplementary material (SOM) of the original paper.
The MINE statistics can be computed for two numeric vectors x and y.
Otherwise a matrix (or data frame) can be provided and two options are available
according to the value of master. If master is a column identifier,
then the MINE statistics are computed for the master variable versus the
other matrix columns. If master is a set of column identifiers, then all
mutual MINE statistics are computed among the column subset.
master, alpha, and C refers respectively to the style,
exp, and c parameters of the original java code.
In the original article, the authors state that the default value α=0.6
(which is the exponent of the search-grid size B(n)=n^{α}) has been
empirically chosen. It is worthwhile noting that alpha and C are
defined to obtain an heuristic approximation in a reasonable amount of time. In case
of small sample size (n) it is preferable to increase alpha to 1 to
obtain a solution closer to the theoretical one.
Value
The Maximal Information-Based Nonparametric Exploration (MINE) statistics
provide quantitative evaluations of different aspects of the relationship
between two variables.
In particular mine returns a list of 5 statistics:
MIC |
Maximal Information Coefficient. |
MAS |
Maximum Asymmetry Score. |
MEV |
Maximum Edge Value. |
MCN |
Minimum Cell Number. |
MIC-R2 |
It is the difference between the MIC value and the Pearson correlation coefficient. |
When computing mine between two numeric vectors x and y,
the output is a list of 5 numeric values. When master is provided,
mine returns a list of 5 matrices having ncol equal to
m. In particular, if master is a single value,
then mine returns a list of 5 matrices having 1 column,
whose rows correspond to the MINE measures between the master
column versus all. Instead if master is a vector of m indices,
then mine output is a list of 5 m-by-m matrices, whose element
i,j corresponds to the MINE statistics computed between the i
and j columns of x.
Author(s)
Michele Filosi and Roberto Visintainer
References
D. Reshef, Y. Reshef, H. Finucane, S. Grossman, G. McVean, P. Turnbaugh,
E. Lander, M. Mitzenmacher, P. Sabeti. (2011)
Detecting novel associations in large datasets.
Science 334, 6062
http://www.exploredata.net
(SOM: Supplementary Online Material at
https://science.sciencemag.org/content/suppl/2011/12/14/334.6062.1518.DC1)
D. Albanese, M. Filosi, R. Visintainer, S. Riccadonna, G. Jurman,
C. Furlanello.
minerva and minepy: a C engine for the MINE suite and its R, Python and MATLAB wrappers.
Bioinformatics (2013) 29(3): 407-408, doi: 10.1093/bioinformatics/bts707.
minepy. Maximal Information-based Nonparametric Exploration in C and Python.
http://minepy.sourceforge.net
Examples
1 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 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 | A <- matrix(runif(50),nrow=5)
mine(x=A, master=1)
mine(x=A, master=c(1,3,5,7,8:10))
x <- runif(10); y <- 3*x+2; plot(x,y,type="l")
mine(x,y)
# MIC = 1
# MAS = 0
# MEV = 1
# MCN = 2
# MIC-R2 = 0
set.seed(100); x <- runif(10); y <- 3*x+2+rnorm(10,mean=2,sd=5); plot(x,y)
mine(x,y)
# rounded values of MINE statistics
# MIC = 0.61
# MAS = 0
# MEV = 0.61
# MCN = 2
# MIC-R2 = 0.13
t <-seq(-2*pi,2*pi,0.2); y1 <- sin(2*t); plot(t,y1,type="l")
mine(t,y1)
# rounded values of MINE statistics
# MIC = 0.66
# MAS = 0.37
# MEV = 0.66
# MCN = 3.58
# MIC-R2 = 0.62
y2 <- sin(4*t); plot(t,y2,type="l")
mine(t,y2)
# rounded values of MINE statistics
# MIC = 0.32
# MAS = 0.18
# MEV = 0.32
# MCN = 3.58
# MIC-R2 = 0.31
# Note that for small n it is better to increase alpha
mine(t,y1,alpha=1)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.59
# MEV = 1
# MCN = 5.67
# MIC-R2 = 0.96
mine(t,y2,alpha=1)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.59
# MEV = 1
# MCN = 5
# MIC-R2 = 0.99
# Some examples from SOM
x <- runif(n=1000, min=0, max=1)
# Linear relationship
y1 <- x; plot(x,y1,type="l"); mine(x,y1)
# MIC = 1
# MAS = 0
# MEV = 1
# MCN = 4
# MIC-R2 = 0
# Parabolic relationship
y2 <- 4*(x-0.5)^2; plot(sort(x),y2[order(x)],type="l"); mine(x,y2)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.68
# MEV = 1
# MCN = 5.5
# MIC-R2 = 1
# Sinusoidal relationship (varying frequency)
y3 <- sin(6*pi*x*(1+x)); plot(sort(x),y3[order(x)],type="l"); mine(x,y3)
# rounded values of MINE statistics
# MIC = 1
# MAS = 0.85
# MEV = 1
# MCN = 4.6
# MIC-R2 = 0.96
# Circle relationship
t <- seq(from=0,to=2*pi,length.out=1000)
x4 <- cos(t); y4 <- sin(t); plot(x4, y4, type="l",asp=1)
mine(x4,y4)
# rounded values of MINE statistics
# MIC = 0.68
# MAS = 0.01
# MEV = 0.32
# MCN = 5.98
# MIC-R2 = 0.68
data(Spellman)
res <- mine(Spellman,master=1,n.cores=1)
## Not run: ## example of multicore computation
res <- mine(Spellman,master=1,n.cores=parallel::detectCores()-1)
## End(Not run)
|
Example output
$MIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MAS
[,1]
[1,] 0
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 0
[8,] 0
[9,] 0
[10,] 0
$MEV
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MCN
[,1]
[1,] 2
[2,] 2
[3,] 2
[4,] 2
[5,] 2
[6,] 2
[7,] 2
[8,] 2
[9,] 2
[10,] 2
$MICR2
[,1]
[1,] -0.02904941
[2,] 0.31966063
[3,] 0.09011389
[4,] 0.26547216
[5,] 0.18254976
[6,] 0.14696220
[7,] 0.65189905
[8,] 0.21821985
[9,] 0.41456301
[10,] 0.62088731
$GMIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$TIC
[,1]
[1,] 0.9709506
[2,] 0.3219281
[3,] 0.4199731
[4,] 0.4199731
[5,] 0.3219281
[6,] 0.9709506
[7,] 0.9709506
[8,] 0.4199731
[9,] 0.4199731
[10,] 0.9709506
$MIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MAS
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0 0 0 0 0 0 0
[2,] 0 0 0 0 0 0 0
[3,] 0 0 0 0 0 0 0
[4,] 0 0 0 0 0 0 0
[5,] 0 0 0 0 0 0 0
[6,] 0 0 0 0 0 0 0
[7,] 0 0 0 0 0 0 0
$MEV
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MCN
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 2 2 2 2 2 2 2
[2,] 2 2 2 2 2 2 2
[3,] 2 2 2 2 2 2 2
[4,] 2 2 2 2 2 2 2
[5,] 2 2 2 2 2 2 2
[6,] 2 2 2 2 2 2 2
[7,] 2 2 2 2 2 2 2
$MICR2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.02904941 0.09011389 0.18254976 0.65189905 0.21821985 0.41456301
[2,] 0.09011389 -0.02904941 -0.09180528 0.15745852 0.13864789 0.41172109
[3,] 0.18254976 -0.09180528 -0.02904941 0.39742169 0.10641182 0.05299923
[4,] 0.65189905 0.15745852 0.39742169 -0.02904941 0.34883796 0.26908462
[5,] 0.21821985 0.13864789 0.10641182 0.34883796 -0.02904941 0.23458887
[6,] 0.41456301 0.41172109 0.05299923 0.26908462 0.23458887 -0.02904941
[7,] 0.62088731 0.03484033 0.39962969 0.24080761 0.28604760 -0.02912810
[,7]
[1,] 0.62088731
[2,] 0.03484033
[3,] 0.39962969
[4,] 0.24080761
[5,] 0.28604760
[6,] -0.02912810
[7,] -0.02904941
$GMIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$TIC
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.9709506 0.4199731 0.3219281 0.9709506 0.4199731 0.4199731 0.9709506
[2,] 0.4199731 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.3219281
[3,] 0.3219281 0.4199731 0.9709506 0.4199731 0.9709506 0.4199731 0.4199731
[4,] 0.9709506 0.4199731 0.4199731 0.9709506 0.4199731 0.4199731 0.4199731
[5,] 0.4199731 0.9709506 0.9709506 0.4199731 0.9709506 0.3219281 0.3219281
[6,] 0.4199731 0.4199731 0.4199731 0.4199731 0.3219281 0.9709506 0.4199731
[7,] 0.9709506 0.3219281 0.4199731 0.4199731 0.3219281 0.4199731 0.9709506
$MIC
[1] 1
$MAS
[1] 0
$MEV
[1] 1
$MCN
[1] 2
$`MIC-R2`
[1] 4.440892e-16
$GMIC
[1] 1
$TIC
[1] 1
$MIC
[1] 0.6099865
$MAS
[1] 0
$MEV
[1] 0.6099865
$MCN
[1] 2
$`MIC-R2`
[1] 0.1292083
$GMIC
[1] 0.6099865
$TIC
[1] 0.6099865
$MIC
[1] 0.6595235
$MAS
[1] 0.3737366
$MEV
[1] 0.6595235
$MCN
[1] 3.321928
$`MIC-R2`
[1] 0.6224055
$GMIC
[1] 0.3662762
$TIC
[1] 3.239177
$MIC
[1] 0.3239506
$MAS
[1] 0.1797499
$MEV
[1] 0.3239506
$MCN
[1] 2.584963
$`MIC-R2`
[1] 0.3151076
$GMIC
[1] 0.1819568
$TIC
[1] 1.852355
$MIC
[1] 1
$MAS
[1] 0.5869921
$MEV
[1] 0.9998182
$MCN
[1] 5.672425
$`MIC-R2`
[1] 0.962882
$GMIC
[1] 0.8704609
$TIC
[1] 84.0454
$MIC
[1] 0.9998182
$MAS
[1] 0.5914029
$MEV
[1] 0.9998182
$MCN
[1] 5
$`MIC-R2`
[1] 0.9909753
$GMIC
[1] 0.6522253
$TIC
[1] 70.02181
$MIC
[1] 1
$MAS
[1] 0
$MEV
[1] 1
$MCN
[1] 2
$`MIC-R2`
[1] 2.664535e-15
$GMIC
[1] 1
$TIC
[1] 147.9999
$MIC
[1] 1
$MAS
[1] 0.6460554
$MEV
[1] 1
$MCN
[1] 2.584963
$`MIC-R2`
[1] 0.9967731
$GMIC
[1] 0.9878122
$TIC
[1] 110.6488
$MIC
[1] 1
$MAS
[1] 0.8636941
$MEV
[1] 1
$MCN
[1] 4.70044
$`MIC-R2`
[1] 0.9582387
$GMIC
[1] 0.8121197
$TIC
[1] 56.29453
$MIC
[1] 0.6829015
$MAS
[1] 0.01067816
$MEV
[1] 0.3219625
$MCN
[1] 3.169925
$`MIC-R2`
[1] 0.6829015
$GMIC
[1] 0.03442878
$TIC
[1] 73.03107
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