An Iterative Algorithm for Regularized Non-negative Matrix Factorizations
We generalize the non-negative matrix factorization algorithm of Lee and Seung to accept a weighted norm, and to support ridge and Lasso regularization. We recast the Lee and Seung multiplicative update as an additive update which does not get stuck on zero values. We apply the companion R package rnnmf to the problem of finding a reduced rank representation of a database of cocktails.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Algorithms for Approximate Subtropical Matrix Factorization
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix fac…
Dimensionality ReductionA Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizations
Given a matrix $X\in \mathbb{R}_+^{m\times n}$ with nonnegative entries, a Positive Semidefinite (PSD) factorization of $X$ is a collection of $r \times r$-dimensional PSD matrices $\{A_i\}$ and $\{B_j\}$ satisfying $X_{…
KL property of exponent $1/2$ of $\ell_{2,0}$-norm and DC regularized factorizations for low-rank matrix recovery
This paper is concerned with the factorization form of the rank regularized loss minimization problem. To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an $\ell_{2…
Multiplicative updates for symmetric-cone factorizations
Given a matrix $X\in \mathbb{R}^{m\times n}_+$ with non-negative entries, the cone factorization problem over a cone $\mathcal{K}\subseteq \mathbb{R}^k$ concerns computing $\{ a_1,\ldots, a_{m} \} \subseteq \mathcal{K}$ …
A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings
Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources po…