Reisinger et al 2010: Spherical Topic Models
Contents
Citation
Joseph Reisinger, Austin Waters, Bryan Silverthorn, and Raymond J. Mooney, "Spherical Topic Models", in Proceedings of the 27th International Conference on Machine Learning (ICML 2010), 2010.
Online version
Summary
This is a recent paper that presents Spherical Mixture Model and Variational Inference methods for Latent Dirichlet Allocation (LDA), which is a Bayesian generative model for general problems in Topic modeling. The highlight of this paper is that it models documents as data points in high-dimensional spherical manifold. Like cosine similarity, the model assumes the data is directional, and can be parameterized by cosine distance and other similarity measures in directional statistics. The authors claim that the spherical topic modeling approach outperforms existing models such as LDA.
Motivations
Traditional topic modeling methods, such as Latent Dirichlet Allocation (LDA), fail to model the presence and the absence of words in the target document, because they assume multinomial distribution for document likelihood. To overcome this issue, the authors propose the Spherical Admixture Model, which models both the frequency as well as the presence and absence of the words. In addition to this, by assuming von Mises-Fisher distribution, they hope to improve the system accuracy when using high-dimensional spherical modeling methods for sparse text data.
Brief Description of the method
This paper first introduces the advantages of von Mises-Fisher distribution for text, then discusses the Spherical Admixture Model and the use of Variational Inference to solve the posterior approximation problem. In this section, we will first summarize the basic characteristics of von Mises-Fisher distribution they assume, then we will introduce the definition of the proposed model, as well as the variational inference method.
von Mises-Fisher Distribution
In LDA, the multinomial distribution of words assigns probabilities to integer vectors of event counts, which is the raw counts of each words in a document in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle &alefsym^{|V|}}
The Spherical Admixture Model
Variation Inference
Dataset and Experiment Settings
[[File:]]
Experimental Results
The authors performed three major experiments. The first experiment is the . The second experiment explores.
Exp
[[File:]]
Exp
[[File:]]
Exp
[[File:]]
Related Papers
This paper is related to many papers in three dimensions.
(1) .
(2) .
(3) .
