Relation between PLSA and NMF and implications

By Éric Gaussier, Cyril Goutte. Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 2005

336 citations recorded by the source corpus.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/049ba736d79c7ae37bc7458e81c5d3926666996c

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In Artificial Intelligence

Citations in the corpus

An analysis of the coherence of descriptors in topic modeling (2015, methodology): “Two common objective functions (Lee & Seung, 2001) used to generate W and H are the Euclidean squared error: and the Kullback–Leibler (KL) divergence, when V and WH both sum to 1 (thus acting as normalized probability distributions): NMF with KL divergence was previously shown to be equivalent to PL”
Optimization for machine learning (2010, methodology): “At this point, it is relevant to mention that it has also been shown by Gaussier and Goutte (2005) that PLSA is equivalent to NMF with the Kullback-Leibler (KL) divergence.”
Convex and Semi-Nonnegative Matrix Factorizations (2010, methodology): “with the Kullback-Leibler (KL) divergence objective has been shown ( 20 ; 13) to be equivalent”
Pseudo-Relevance Feedback Based on Matrix Factorization (2016, neutral): “, document clustering [2], document summarization [17], and probabilistic latent semantic indexing [9].”
Recognising realistic emotions and affect in speech: State of the art and lessons learnt from the first challenge (2011, methodology): “NMF, a method strictly related to probabilistic latent semantic analysis (Gaussier and Goutte, 2005), is a recent alternative to PCA in which the data and components are assumed to be non-negative: NMF learns to represent emotional classes with a set of basic emotional subclasses.”
The Why and How of Nonnegative Matrix Factorization (2014, background): “Note that NMF is closely related to existing topic models, in particular probabilistic latent semantic analysis and indexing (PLSA and PLSI) [45, 37].”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “Further more, NMF is equivalent to k-means clustering when using Square of Euclidian Distance (SED) [44], [45], while tantamount to Probabilistic Latent Semantic Analysis (PLSA) when using Generalized Kullback-Leibler Divergence (GKLD) as the objective function [46], [47].”
On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing (2008, background): “Gaussier and Goutte (2005) made the initial connection between NMF and PLSI, by showing that the iterative update procedures of PLSI and NMF are similar in that the fixed-point equations for the converged solutions are the same.”
Aggregating Continuous Word Embeddings for Information Retrieval (2013, methodology): “The PLSA model proposed by Hoffman (Hofmann, 1999) can be thought of as a constrained matrix factorization problem equivalent to NMF (Lee and Seung, 1999; Gaussier and Goutte, 2005).”
Comment-based multi-view clustering of web 2.0 items (2014, background): “Some theoretical studies [13, 15] have shown the equivalence between NMF with other clustering algorithms, including K -means, Spectral Clustering and PLSA, with additional constraints.”
Graph Regularized Nonnegative Matrix Factorization for Data Representation (2011, background): “3) Recent studies [17], [13] show that NMF is closely related to Probabilistic Latent Semantic Analysis (PLSA) [21].”
A Semi-NMF-PCA Unified Framework for Data Clustering (2017, background): “Gaussier and Goutte [16] established links between NMF and PLSA, and they claimed that PLSA solves NMF with KL I-divergence, and for this cost function, PLSA provides a better consistency.”
Outlier Detection for Text Data (2017, methodology): “Other than applications of NMF in the text domain, Gaussier and Goutte [10] established the equivalence between NMF and pLSA.”
Constrained Nonnegative Matrix Factorization for Image Representation (2012, methodology): “Especially, PLSA solves the problem of NMF with KL divergence [19], [20].”
Multi-View Clustering via Joint Nonnegative Matrix Factorization (2013, background): “Therefore there could be many possible solutions, and it is important to enforce additional constraints to ensure the uniqueness of the factorization in clustering.”
Unsupervised learning of auditory filter banks using non-negative matrix factorisation (2008, neutral): “In [5] it is proven that a point which is invariant under these up-date rules is also invariant under the update formulas of the algorithm proposed in [6] for probabilistic latent semantic analysis (PLSA).”