# Topic Modeling Algorithms (LDA, NMF, PLSA)

## What are Topic Modeling Algorithms?

Topic Modeling Algorithms are unsupervised machine learning techniques used to discover hidden thematic structures or topics within a large collection of documents. Some popular Topic Modeling Algorithms include Latent Dirichlet Allocation (LDA), Non-negative Matrix Factorization (NMF), and Probabilistic Latent Semantic Analysis (PLSA).

### Latent Dirichlet Allocation (LDA):

#### What is LDA?

Latent Dirichlet Allocation (LDA) is a generative probabilistic model introduced by Blei et al. in 2003. LDA assumes that each document in a corpus is a mixture of a small number of topics, and each topic is a distribution over words.

#### How does LDA work?

LDA works by iteratively updating the topic-word and document -topic distributions to maximize the likelihood of observing the given corpus. The algorithm uses Bayesian inference with Dirichlet priors to estimate these distributions.

### Non-negative Matrix Factorization (NMF):

#### What is NMF?

Non-negative Matrix Factorization (NMF) is a linear algebraic method that decomposes a non-negative matrix into two lower-dimensional non-negative matrices. In the context of Topic Modeling, NMF is used to approximate the document-term matrix by finding latent topics.

#### How does NMF work?

NMF works by minimizing the reconstruction error between the original matrix and the product of the two lower-dimensional matrices. The algorithm iteratively updates the matrices using multiplicative update rules until convergence.

### Probabilistic Latent Semantic Analysis (PLSA):

#### What is PLSA?

Probabilistic Latent Semantic Analysis (PLSA), also known as Probabilistic Latent Semantic Indexing (PLSI), is a generative statistical model introduced by Hofmann in 1999. PLSA models the co-occurrence of words and documents as a mixture of topics.

#### How does PLSA work?

PLSA uses the Expectation-Maximization (EM) algorithm to estimate the topic-word and document-topic distributions. The algorithm iteratively refines these distributions to maximize the likelihood of the observed document-word co-occurrences.

## Some benefits of using Topic Modeling Algorithms

• Unsupervised learning: Topic Modeling Algorithms can discover hidden patterns in text data without the need for labeled training data.
• Dimensionality reduction: Topic Modeling Algorithms reduce the dimensionality of text data, making it more manageable and easier to analyze.
• Text categorization: Topic Modeling Algorithms can be used to automatically categorize or group documents based on their underlying topics.