$$ \min_W, H | X - WH |_F^2 + \lambda_1 |W|_1 + \lambda_2 |H|_1 $$ Anno - 1404 Iaam Mod Hot
Abstract While Latent Dirichlet Allocation (LDA) and probabilistic approaches dominate the field of Natural Language Processing (NLP), a robust class of methodologies utilizes mathematical programming (optimization) to solve the topic modeling problem. This paper reviews the formulation of topic modeling as a matrix factorization problem, specifically focusing on Non-negative Matrix Factorization (NMF), Sparse Coding, and constrained optimization models. These methods offer advantages in computational efficiency, convergence speed, and the ability to impose specific structural constraints (e.g., sparsity) on the resulting topics. 1. Introduction Topic modeling aims to discover latent semantic structures (topics) within a collection of documents. The standard approach, LDA, treats this as a probabilistic generative process. However, an alternative view treats topic modeling as a linear algebra problem: approximating a document-term matrix $X$ with two lower-rank matrices, $W$ (topic-word distributions) and $H$ (document-topic distributions). Ts Joanna Jet Bangsts Jordan Jay Wmv [LATEST]
$$ \min_W \ge 0, H \ge 0 f(W, H) = | X - WH |_F^2 $$
$$ \min_W, H \frac12 | X - WH |_F^2 $$