# probabilistic Latent Semantic Analysis

(45 minutes to learn)

## Summary

Probabilistic Latent Semantic Analysis (pLSA), also known as probabilistic Latent Semantic Indexing (pLSI), is a matrix decomposition technique for binary and count data, where one component of the data is conditionally independent of the other component given some unobserved factor. pLSA is most commonly used for document modeling, where the count data is the number of times a term appears in each document (forming an observed term by document count matrix), and the factors are interpreted as the latent/unobserved topics.

## Context

This concept has the prerequisites:

- latent semantic analysis
- maximum likelihood (pLSA is fit using maximum likelihood.)
- optimization problems (Finding the optimal solution requires solving an optimization problem.)

## Goals

- Understand the difference between pLSA and LSA
- Why is pLSA considered a statistical model while LSA is not?
- What objective function does pLSA maximize in order to determine the decomposition?

- How would a trained pLSA model handle new documents? (see Blei et al.'s LDA paper)

## Core resources (read/watch one of the following)

## -Free-

→ Bayesian Reasoning and Machine Learning

A textbook for a graudate machine learning course.

Location:
Section 15.6.1 pgs. 323-325

Additional dependencies:

- Expectation-Maximization algorithm

Other notes:

- presents the expectation-maximization algorithm for learning the matrix decomposition, which is the standard technique for learning the decomposition

→ Probabilistic Latent Semantic Indexing

Other notes:

- You can gloss over section 3 if you're not familiar with the expectation maximization algorithm

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Latent Dirichlet Allocation (2003)

The research paper that introduced latent Dirichlet allocation.

Location:
Section 4.3 pgs. 1000-1001

Other notes:

- points out some of the weaknesses of pLSA

## See also

- Latent Dirichlet allocation is a fully Bayesian version of pLSA.
- A pLSA matrix decomposition is typically learned using the expectation maximization algorithm.