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.

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)
``` |

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