vertices_est: The vertex hunting in the Topic SCORE algorithm
In TopicScore: The Topic SCORE Algorithm to Fit Topic Models

Description Usage Arguments Value Author(s) References Examples

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.

1	vertices_est(R, K0, m, num_restart)

`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.

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.

Minzhe Wang

Ke, Z. T., & Wang, M. (2017). A new SVD approach to optimal topic estimation. arXiv preprint arXiv:1704.07016.

# 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)