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

## 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

 `1` ```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.

Minzhe Wang

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# 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) ```

TopicScore documentation built on June 6, 2019, 5:06 p.m.