logisticPCA-package

Description

Dimension reduction techniques for binary data including logistic PCA

Author(s)

Andrew J. Landgraf

Convex Logistic Principal Component Analysis

Description

Dimensionality reduction for binary data by extending Pearson's PCA formulation to minimize Binomial deviance. The convex relaxation to projection matrices, the Fantope, is used.

Usage

convexLogisticPCA(x, k = 2, m = 4, quiet = TRUE, partial_decomp = FALSE,
  max_iters = 1000, conv_criteria = 1e-06, random_start = FALSE, start_H,
  mu, main_effects = TRUE, ss_factor = 4, weights, M)

Arguments

Value

An S3 object of class clpca which is a list with the following components:

References

Landgraf, A.J. & Lee, Y., 2015. Dimensionality reduction for binary data through the projection of natural parameters. arXiv preprint arXiv:1510.06112.

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4)

CV for convex logistic PCA

Description

Run cross validation on dimension and m for convex logistic PCA

Usage

cv.clpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)

Arguments

Value

A matrix of the CV negative log likelihood with k in rows and m in columns

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.clpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

CV for logistic PCA

Description

Run cross validation on dimension and m for logistic PCA

Usage

cv.lpca(x, ks, ms = seq(2, 10, by = 2), folds = 5, quiet = TRUE, Ms, ...)

Arguments

Value

A matrix of the CV negative log likelihood with k in rows and m in columns

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(mat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

CV for logistic SVD

Description

Run cross validation on dimension for logistic SVD

Usage

cv.lsvd(x, ks, folds = 5, quiet = TRUE, ...)

Arguments

Value

A matrix of the CV negative log likelihood with k in rows

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lsvd(mat, ks = 1:9)
plot(negloglikes)

## End(Not run)

Fitted values using logistic PCA

Description

Fit a lower dimentional representation of the binary matrix using logistic PCA

Usage

## S3 method for class 'lpca'
fitted(object, type = c("link", "response"), ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# construct fitted probability matrix
fit = fitted(lpca, type = "response")

Fitted values using logistic SVD

Description

Fit a lower dimentional representation of the binary matrix using logistic SVD

Usage

## S3 method for class 'lsvd'
fitted(object, type = c("link", "response"), ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# construct fitted probability matrix
fit = fitted(lsvd, type = "response")

United States Congressional Voting Records 1984

Description

This data set includes votes for each of the U.S. House of Representatives Congressmen on the 16 key votes identified by the CQA. The CQA lists nine different types of votes: voted for, paired for, and announced for (these three simplified to yea), voted against, paired against, and announced against (these three simplified to nay), voted present, voted present to avoid conflict of interest, and did not vote or otherwise make a position known (these three simplified to an unknown disposition).

Usage

house_votes84

Format

A matrix with all binary or missing entries. There are 435 rows corresponding members of congress and 16 columns representing the bills being voted on. The row names refer to the political party of the members of congress

Source

Congressional Quarterly Almanac, 98th Congress, 2nd session 1984, Volume XL: Congressional Quarterly Inc., Washington, D.C., 1985

Data converted to a matrix from:

Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

Examples

data(house_votes84)
congress_lpca = logisticPCA(house_votes84, k = 2, m = 4)

Inverse logit for matrices

Description

Apply the inverse logit function to a matrix, element-wise. It generalizes the inv.logit function from the gtools library to matrices

Usage

inv.logit.mat(x, min = 0, max = 1)

Arguments

Examples

(mat = matrix(rnorm(10 * 5), nrow = 10, ncol = 5))
inv.logit.mat(mat)

Bernoulli Log Likelihood

Description

Calculate the Bernoulli log likelihood of matrix

Usage

log_like_Bernoulli(x, theta, q)

Arguments

Logistic Principal Component Analysis

Description

Dimensionality reduction for binary data by extending Pearson's PCA formulation to minimize Binomial deviance

Usage

logisticPCA(x, k = 2, m = 4, quiet = TRUE, partial_decomp = FALSE,
  max_iters = 1000, conv_criteria = 1e-05, random_start = FALSE, start_U,
  start_mu, main_effects = TRUE, validation, M, use_irlba)

Arguments

Value

An S3 object of class lpca which is a list with the following components:

References

Landgraf, A.J. & Lee, Y., 2015. Dimensionality reduction for binary data through the projection of natural parameters. arXiv preprint arXiv:1510.06112.

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

# Logistic PCA likely does a better job finding latent features
# than standard PCA
plot(svd(mat_logit)$u[, 1], lpca$PCs[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])

Logistic Singular Value Decomposition

Description

Dimensionality reduction for binary data by extending SVD to minimize binomial deviance.

Usage

logisticSVD(x, k = 2, quiet = TRUE, max_iters = 1000,
  conv_criteria = 1e-05, random_start = FALSE, start_A, start_B, start_mu,
  partial_decomp = TRUE, main_effects = TRUE, use_irlba)

Arguments

Value

An S3 object of class lsvd which is a list with the following components:

References

de Leeuw, Jan, 2006. Principal component analysis of binary data by iterated singular value decomposition. Computational Statistics & Data Analysis 50 (1), 21–39.

Collins, M., Dasgupta, S., & Schapire, R. E., 2001. A generalization of principal components analysis to the exponential family. In NIPS, 617–624.

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

# Logistic SVD likely does a better job finding latent features
# than standard SVD
plot(svd(mat_logit)$u[, 1], lsvd$A[, 1])
plot(svd(mat_logit)$u[, 1], svd(mat)$u[, 1])

Plot convex logistic PCA

Description

Plots the results of a convex logistic PCA

Usage

## S3 method for class 'clpca'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run convex logistic PCA on it
clpca = convexLogisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(clpca)

## End(Not run)

Plot CV for logistic PCA

Description

Plot cross validation results logistic PCA

Usage

## S3 method for class 'cv.lpca'
plot(x, ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

## Not run: 
negloglikes = cv.lpca(dat, ks = 1:9, ms = 3:6)
plot(negloglikes)

## End(Not run)

Plot logistic PCA

Description

Plots the results of a logistic PCA

Usage

## S3 method for class 'lpca'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 2, m = 4, main_effects = FALSE)

## Not run: 
plot(lpca)

## End(Not run)

Plot logistic SVD

Description

Plots the results of a logistic SVD

Usage

## S3 method for class 'lsvd'
plot(x, type = c("trace", "loadings", "scores"), ...)

Arguments

Examples

# construct a low rank matrix in the logit scale
rows = 100
cols = 10
set.seed(1)
mat_logit = outer(rnorm(rows), rnorm(cols))

# generate a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0

# run logistic SVD on it
lsvd = logisticSVD(mat, k = 2, main_effects = FALSE, partial_decomp = FALSE)

## Not run: 
plot(lsvd)

## End(Not run)

Predict Convex Logistic PCA scores or reconstruction on new data

Description

Predict Convex Logistic PCA scores or reconstruction on new data

Usage

## S3 method for class 'clpca'
predict(object, newdata, type = c("PCs", "link", "response"),
  ...)

Arguments

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
clpca = convexLogisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(clpca, mat_new)

Predict Logistic PCA scores or reconstruction on new data

Description

Predict Logistic PCA scores or reconstruction on new data

Usage

## S3 method for class 'lpca'
predict(object, newdata, type = c("PCs", "link", "response"),
  ...)

Arguments

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lpca = logisticPCA(mat, k = 1, m = 4, main_effects = FALSE)

PCs = predict(lpca, mat_new)

Predict Logistic SVD left singular values or reconstruction on new data

Description

Predict Logistic SVD left singular values or reconstruction on new data

Usage

## S3 method for class 'lsvd'
predict(object, newdata, quiet = TRUE, max_iters = 1000,
  conv_criteria = 1e-05, random_start = FALSE, start_A, type = c("PCs",
  "link", "response"), ...)

Arguments

Details

Minimizes binomial deviance for new data by finding the optimal left singular vector matrix (A), given B and mu. Assumes the columns of the right singular vector matrix (B) are orthonormal.

Examples

# construct a low rank matrices in the logit scale
rows = 100
cols = 10
set.seed(1)
loadings = rnorm(cols)
mat_logit = outer(rnorm(rows), loadings)
mat_logit_new = outer(rnorm(rows), loadings)

# convert to a binary matrix
mat = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit)) * 1.0
mat_new = (matrix(runif(rows * cols), rows, cols) <= inv.logit.mat(mat_logit_new)) * 1.0

# run logistic PCA on it
lsvd = logisticSVD(mat, k = 1, main_effects = FALSE, partial_decomp = FALSE)

A_new = predict(lsvd, mat_new)

Project onto the Fantope

Description

Project a symmetric matrix onto the convex set of the rank k Fantope

Usage

project.Fantope(x, k)

Arguments

Value