Topic space

As explained in Math and Architectures of Deep Learning

The reduced vector space whose coordinates are topic dimensions rather than original terms.

A topic space is a reduced vector space whose coordinates represent latent topics rather than individual terms. It gives each document a compact topic-based representation. section 4.6.2

Latent semantic analysis selects the strongest topic dimensions from the eigenvalues of XᵀX, discards weaker dimensions, and retains the corresponding columns of V. If t topics remain, V is m × t; projecting the original document-term matrix X into V produces an m × t document-topic matrix. section 4.6.2

Cosine similarity between rows in topic space can reveal indirect document connections that are hidden when similarity is computed directly from the original term vectors. section 4.6.2

Figure 4.6 Document vectors from our toy dataset d₀, ⋯ d₆. Each word in the vocabulary corresponds to a separate dimension. Dots show projections of document feature vectors on the plane formed by the axes corresponding to the terms gun(s) and violence.

Visualize document vectors as points in a term-coordinate space before dimensionality reduction, then interpret topic space as a lower-dimensional representation. section 4.6.2

How Math and Architectures of Deep Learning covers it

How deep it goes

Defines eigenvalue-based dimension selection and matrix projection, then stops short of implementation details.

Examples

Uses toy document vectors and a document-term matrix containing terms such as violence, gun, America, and roses.

What it assumes

Assumes document-term vectors and matrix operations, while developing eigenvalue-based dimensionality reduction.

What you can do after

Evaluate document similarity using reduced topic representations and cosine similarity.

How it connects

Connects latent semantic analysis, eigenvalues, dimensionality reduction, document-term matrices, and cosine similarity.

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Related concepts

• projectionproduced by · A projection is a mapping or operation that produces a selected or derived representation of an input, often by retaining specified components or mapping it to a subspace.
• cosine similaritycontrasts with · Cosine similarity measures the directional alignment of two nonzero vectors as the cosine of the angle between them, equivalently their dot product divided by the product of their magnitudes.

This explainer was generated by Manning's knowledge graph from the text of Math and Architectures of Deep Learning. The section links point to the parts of the book it draws on.