gmf: General Matrix Factorization

In EMMIXmfa: Mixture Models with Component-Wise Factor Analyzers

General Matrix Factorization

Description

Performs a matrix factorization on the given data set. The factorization is done using a stochastic gradient decent method.

Usage

gmf(Y, q, maxit = 1000, lambda = 0.01, cor_rate = 0.9)

Arguments

Y	data matrix containing all numerical values.
maxit	maximum number of iterations.
q	number of factors.
lambda	initial learning rate.
cor_rate	correction rate.

Details

Unsupervised matrix factorization of a n \times p data matrix Y can be expressed as,

Y^{\top} \approx A B^{\top},

where A is a p \times q matrix and B is n \times q matrix. With this matrix factorization method, one replaces the ith row in matrix Y by the ith row in matrix B. The matrices A and B are chosen to minimize an objective function f(Y, A, B) with under constraints specific to the matrix factorization method.

It is imperative that columns of the data matrix be on the same scale. Otherwise, it may not be possible to obtain a factorization of the data using this approach.

Value

A list containing,

A	A numeric matrix of size p \times q
B	A numeric matrix of size n \times q matrix

References

Nikulin V, Huang T-H, Ng SK, Rathnayake SI, & McLachlan GJ (2011). A very fast algorithm for matrix factorization. Statistics & Probability Letters 81, 773–782.

Examples

lst <- gmf(iris[, -5], q = 2, maxit = 100)

EMMIXmfa documentation built on May 29, 2024, 11:15 a.m.