LSA is a technique that analyzes relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. It uses a mathematical technique called Singular Value Decomposition (SVD) to reduce the dimensionality of the term-document matrix while preserving the similarity structure among documents.
#How it Works
- Term-Document Matrix Construction:
- Create a matrix where each row represents a unique word and each column represents a document.
- The entries in the matrix can be raw counts, term frequency (TF), or term frequency-inverse document frequency (TF-IDF) values.
- Singular Value Decomposition (SVD):
- Apply SVD to the term-document matrix to decompose it into three matrices: $U$, $\Sigma$, and $V^T$.
- $U$ represents the term-topic matrix.
- $\Sigma$ is a diagonal matrix of singular values.
- $V^T$ represents the document-topic matrix.
- Dimensionality Reduction:
- Reduce the number of dimensions by keeping only the top $k$ singular values and their corresponding vectors in $U$ and $V^T$.
- This results in a lower-dimensional approximation of the original term-document matrix.
- Topic Interpretation:
- The reduced matrices can be used to identify topics and the relationships between terms and documents.
#Advantages
- Effective in capturing synonymy and polysemy.
- Reduces noise and redundancy in the data.
#Limitations
- The resulting topics are not easily interpretable.
- Assumes a linear relationship between terms and documents.
#Comparison with LDA
- LSA is based on linear algebra and dimensionality reduction, while LDA is based on probabilistic modeling.
- LSA is simpler and faster but less interpretable, whereas LDA provides more interpretable topics but is computationally more demanding.
- LSA can handle synonymy and polysemy to some extent, but LDA explicitly models the generative process of documents, making it more robust in capturing the underlying topic structure.
Latent Dirichlet Allocation (LDA)