vertices_est {TopicScore}

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)