| Title: | The Topic SCORE Algorithm to Fit Topic Models |
| Version: | 0.0.1 |
| Description: | Provides implementation of the "Topic SCORE" algorithm that is proposed by Tracy Ke and Minzhe Wang. The singular value decomposition step is optimized through the usage of svds() function in 'RSpectra' package, on a 'dgRMatrix' sparse matrix. Also provides a column-wise error measure in the word-topic matrix A, and an algorithm for recovering the topic-document matrix W given A and D based on quadratic programming. The details about the techniques are explained in the paper "A new SVD approach to optimal topic estimation" by Tracy Ke and Minzhe Wang (2017) <doi:10.48550/arXiv.1704.07016>. |
| Depends: | R (≥ 3.5.0) |
| License: | MIT + file LICENSE |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| Imports: | utils, stats, graphics, RSpectra, combinat, quadprog, methods, Matrix, slam |
| Author: | Minzhe Wang [aut, cre], Tracy Ke [aut] |
| Maintainer: | Minzhe Wang <minzhew@uchicago.edu> |
| NeedsCompilation: | no |
| Packaged: | 2019-06-04 15:32:17 UTC; greenlink |
| Repository: | CRAN |
| Date/Publication: | 2019-06-06 11:12:14 UTC |
Associated Press data
Description
Associated Press data from the First Text Retrieval Conference (TREC-1) 1992, which has being processed by stop-words removal, low-frequency words removal and short documents removal.
Usage
data("AP")
Format
The data set is an object of class "simple_triplet_matrix" provided by package slam.
It is a word-document matrix which contains the term frequency of 7000 words in 2134 documents.
Source
Harman, D. (1992, November). Overview of the First Text REtrieval Conference (TREC-1). In TREC (Vol. 1992, pp. 1-20).
Estimation of W from A and X
Description
This function estimates the topic-document matrix W from the word-topic matrix A and the word-document X through quadratic programming.
Usage
W_from_AD(A, X)
Arguments
A |
The p-by-K word-topic matrix. |
X |
The p-by-n word-document matrix. |
Value
The estimated K-by-n topic-document matrix W_hat.
Author(s)
Minzhe Wang
Examples
data("AP")
K <- 3
tscore_obj <- topic_score(K, AP)
W_hat <- W_from_AD(tscore_obj$A_hat, AP)
The l_1 distance between two thin matrices up to a column permuation
Description
This function computes l_1 distance between two thin matrices up to a column permuation, that is to find the smallest sum of absolute value entry-wise difference between two matrices over all possible permutations over the columns of the first matrix. This can be done either universially or greedily.
Usage
error_A(A, A_hat, type = "u")
Arguments
A |
The first p-by-K matrix. |
A_hat |
The second p-by-K matrix. |
type |
The search type for the best permutation. If it's 'u', the search is done universially, that is over all possible permuations of the columns of A. If it's 'g', the search is done greedily, that is at kth step find the closest column in the remaining columns of A to the kth column of A_hat in terms of l_1 distance. Greedy search may result in sub-optimal solutions, but it can be computed much faster than the universal way when K is large. The default value is 'u'. |
Value
The l_1 distance.
Author(s)
Minzhe Wang
Examples
# The example uses the runif() function in the 'stats' package
A <- matrix(runif(10*3),10,3)
A_hat <- A + 0.1*matrix(runif(10*3),10,3)
error_A(A, A_hat)
error_A(A, A_hat, type='g')
The l_2 distance between a point and a simplex
Description
This function computes the l_2 distance between a point and a simplex, that is the shortest l_2 distance between the given point and any point in the simplex.
Usage
simplex_dist(theta, V)
Arguments
theta |
A (K-1) dimensional vector, representing a point. |
V |
The K-by-(K-1) vertices matrix, with each row being a vertex. |
Value
The l_2 distance.
Author(s)
Minzhe Wang
References
Ke, Z. T., & Wang, M. (2017). A new SVD approach to optimal topic estimation. arXiv preprint arXiv:1704.07016.
Examples
# Generate 3 vertices
V <- rbind(c(-1/2,-1/2), c(1,0), c(0,1))
theta <- c(3,1)
simplex_dist(theta, V)
The Topic SCORE algorithm
Description
This function obtains the word-topic matrix A from the word-document matrix X through the Topic SCORE algorithm.
Usage
topic_score(K, X, K0, m, Mquantile = 0, scatterplot = FALSE,
num_restart = 1, seed = NULL)
Arguments
K |
The number of topics. |
X |
The p-by-n word-document matrix, with each column being a distribution over a fixed set of vocabulary.
This matrix can be of class |
K0 |
The number of greedy search steps in vertex hunting. If the value is missing it will be set to ceiling(1.5*K). |
m |
The number of centers in the kmeans step in vertex hunting. If the value is missing it will be set to 10*K. |
Mquantile |
The percentage of the quantile of the diagonal entries of matrix M, which is used to upper truncate the diagonal entries of matirx M. When it's 0, it will degenerate the case when there is no normalization. When it's 1, it means there is no truncation. Default is 0. |
scatterplot |
Whether a scatterplot of rows of R will be generated. |
num_restart |
The number of random restart in the kmeans step in vertex hunting. Default is 1. |
seed |
The random seed. Default value is NULL. |
Value
A list containing
- A_hat
The estimated p-by-K word-topic matrix.
- R
The p-by-(K-1) left singular vector ratios matrix.
- V
The K-by-(K-1) vertices matrix, with each row being a vertex found through the vertex hunting algorithm in the simplex formed by the rows of R.
- Pi
The p-by-K convex combinations matrix, with each row being the convex combination coefficients of a row of R using V as vertices.
- theta
The K0-by-(K-1) matrix of K0 potential vertices found in the greedy step of the vertex hunting algorithm.
Author(s)
Minzhe Wang
References
Ke, Z. T., & Wang, M. (2017). A new SVD approach to optimal topic estimation. arXiv preprint arXiv:1704.07016.
Examples
data("AP")
K <- 3
tscore_obj <- topic_score(K, AP)
# Visualize the result
plot(tscore_obj$R[,1], tscore_obj$R[,2])
The vertex hunting in the Topic SCORE algorithm
Description
This function conducts the vertex hunting in the Topic SCORE algorithm. More generally this function finds a simplex with K vertices that best approximates the given p data points in a (K-1) dimensional space.
Usage
vertices_est(R, K0, m, num_restart)
Arguments
R |
The p-by-(K-1) data matrix, with each row being a data point. |
K0 |
The number of greedy search steps. |
m |
The number of centers in the kmeans step. |
num_restart |
The number of random start in the kmeans step. |
Value
A list containing
- V
The K-by-(K-1) vertices matrix, with each row being a vertex in the found simplex.
- theta
The K0-by-(K-1) matrix of potential K0 vertices found in the greedy step.
Author(s)
Minzhe Wang
References
Ke, Z. T., & Wang, M. (2017). A new SVD approach to optimal topic estimation. arXiv preprint arXiv:1704.07016.
Examples
# Generate 3 vertices
V <- rbind(c(-1/2,-1/2), c(1,0), c(0,1))
# Randomly generate the convex combination weights of 1000 points
Pi <- matrix(runif(3*1000),3,1000)
Pi <- apply(Pi, 2, function(x){x/sum(x)})
R <- t(Pi)%*%V
v_est_obj <- vertices_est(R, 1.5*3, 10*3, 1)
# Visualize the result
plot(R[,1], R[,2])
points(v_est_obj$V[,1], v_est_obj$V[,2], col=2, lwd=5)