Package 'mmtsne'

Estimate perplexity and probability values

Description

hbeta returns the perplexity and probability values for a row of data D.

Usage

hbeta(D, beta = 1)

Arguments

D	A distance vector.
beta	A constant scalar.

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Multiple maps t-SNE

Description

mmtsne estimates a multiple maps t-distributed stochastic neighbor embedding (multiple maps t-SNE) model.

Usage

mmtsne(X, no_maps = 1, no_dims = 2, perplexity = 30, max_iter = 500,
  momentum = 0.5, final_momentum = 0.8, mom_switch_iter = 250,
  eps = 1e-07)

Arguments

X	A dataframe or matrix of $N$ rows and $D$ columns.
no_maps	The number of maps (positive whole number) to be estimated.
no_dims	The number of dimensions per map. Typical values are 2 or 3.
perplexity	The target perplexity for probability matrix construction. Commonly recommended values range from 5 to 30. Perplexity roughly corresponds to the expected number of neighbors per data point.
max_iter	The number of iterations to run.
momentum	Constant scaling factor for update momentum in gradient descent algorithm.
final_momentum	Constant scaling factor for update momentum in gradient descent algorithm after the momentum switch point.
mom_switch_iter	The iteration at which momentum switches from momentum to final_momentum.
eps	A small positive value near zero.

Details

mmtsne is a wrapper that performs multiple maps t-SNE on an input dataset, X. The function will pre-process X, an $N$ by $D$ matrix or dataframe, then call mmtsneP. The pre-processing steps include calls to x2p and p2sp to convert X into an $N$ by $N$ symmetrical joint probability matrix.

The mmtnseP code is an almost direct port of the original multiple maps t-SNE Matlab code by van der Maaten and Hinton (2012). mmtsne estimates a multidimensional array of N x no_dims x no_maps. Each map is an N x no_dims matrix of estimated t-SNE coordinates. When no_maps=1, multiple maps t-SNE reduces to standard t-SNE.

Value

A list that includes the following objects:

Y

An N x no_dims x no_maps array of predicted coordinates.

weights

An N x no_maps matrix of unscaled weights. A high weight on entry $i, j$ indicates a greater contribution of point $i$ on map $j$.

proportions

An N x no_maps matrix of scaled weights. A high weight on entry $i, j$ indicates a greater contribution of point $i$ on map $j$.

References

L.J.P. van der Maaten and G.E. Hinton. “Visualizing Non-Metric Similarities in Multiple Maps.” Machine Learning 87(1):33-55, 2012. PDF.

Examples

# Load the iris dataset
data("iris")

# Estimate a mmtsne model with 2 maps, 2 dimensions each
model <- mmtsne(iris[,1:4], no_maps=2, max_iter=100)

# Plot the results side-by-side for inspection
# Points scaled by map proportion weights plus constant factor
par(mfrow=c(1,2))
plot(model$Y[,,1], col=iris$Species, cex=model$proportions[,1] + .2)
plot(model$Y[,,2], col=iris$Species, cex=model$proportions[,2] + .2)
par(mfrow=c(1,1))

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Multiple maps t-SNE with symmetric probability matrix

Description

mmtsneP estimates a multiple maps t-distributed stochastic neighbor embedding (multiple maps t-SNE) model.

Usage

mmtsneP(P, no_maps, no_dims = 2, max_iter = 500, momentum = 0.5,
  final_momentum = 0.8, mom_switch_iter = 250, eps = 1e-07)

Arguments

P	An $N x N$ symmetric joint probability distribution matrix. These can be constructed from an $N$ by $D$ matrix with x2p and p2sp. Alternatively, the wrapper function mmtsne will wrap the matrix construction and multiple maps t-SNE model estimation into a single step.
no_maps	The number of maps (positive whole number) to be estimated.
no_dims	The number of dimensions per map. Typical values are 2 or 3.
max_iter	The number of iterations to run.
momentum	Constant scaling factor for update momentum in gradient descent algorithm.
final_momentum	Constant scaling factor for update momentum in gradient descent algorithm after the momentum switch point.
mom_switch_iter	The iteration at which momentum switches from momentum to final_momentum.
eps	A small positive value near zero.

Details

This code is an almost direct port of the original multiple maps t-SNE Matlab code by van der Maaten and Hinton (2012). mmtsne estimates a multidimensional array of N x no_dims x no_maps. Each map is an N x no_dims matrix of estimated t-SNE coordinates. When no_maps=1, multiple maps t-SNE reduces to standard t-SNE.

Value

A list that includes the following objects:

Y

An N x no_dims x no_maps array of predicted coordinates.

weights

An N x no_maps matrix of unscaled weights. A high weight on entry $i, j$ indicates a greater contribution of point $i$ on map $j$.

proportions

An N x no_maps matrix of scaled weights. A high weight on entry $i, j$ indicates a greater contribution of point $i$ on map $j$.

References

L.J.P. van der Maaten and G.E. Hinton. “Visualizing Non-Metric Similarities in Multiple Maps.” Machine Learning 87(1):33-55, 2012. PDF.

Examples

# Load the iris dataset
data("iris")

# Produce a symmetric joint probability matrix
prob_matrix <- p2sp(x2p(as.matrix(iris[,1:4])))

# Estimate a mmtsne model with 2 maps, 2 dimensions each
model <- mmtsneP(prob_matrix, no_maps=2, max_iter=100)

# Plot the results side-by-side for inspection
# Points scaled by map proportion weights plus constant factor
par(mfrow=c(1,2))
plot(model$Y[,,1], col=iris$Species, cex=model$proportions[,1] + 0.2)
plot(model$Y[,,2], col=iris$Species, cex=model$proportions[,2] + 0.2)
par(mfrow=c(1,1))

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Probability matrix to symmetric probability matrix

Description

p2sp returns a symmetrical pair-wise joint probability matrix given an input probability matrix P.

Usage

p2sp(P)

Arguments

P	An N x N probability matrix, like those produced by x2p

Value

An N x N symmetrical matrix of pair-wise probabilities.

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Data to probability matrix

Description

x2p returns a pair-wise conditional probability matrix given an input matrix X.

Usage

x2p(X, perplexity = 30, tol = 1e-05)

Arguments

X	A data matrix with $N$ rows.
perplexity	The target perplexity. Values between 5 and 50 are generally considered appropriate. Loosely translates into the expected number of neighbors per point.
tol	A small positive value.

Details

This function is an almost direct port of the original Python implementation by van der Maaten and Hinton (2008). It uses a binary search to estimate probability values for all pairwise-elements of X. The conditional Gaussian distributions should all be of equal perplexity.

Value

An N x N matrix of pair-wise probabilities.

References

L.J.P. van der Maaten and G.E. Hinton. “Visualizing High-Dimensional Data Using t-SNE.” Journal of Machine Learning Research 9(Nov):2579-2605, 2008. PDF.

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