How deeply does Math and Architectures of Deep Learning cover topic vector?

Explains term contributions, eigenvector construction, topic weighting, cutoff selection, projection, and cosine similarity.

Topic vector

As explained in Math and Architectures of Deep Learning

A vector whose entries indicate how strongly each term contributes to a topic.

A topic vector is a column of V whose entries show how strongly the vocabulary terms contribute to one latent topic. In latent semantic analysis, topic vectors provide a lower-dimensional topic space for representing documents. section 4.6.2

Topic vectors support dimensionality reduction through this workflow:

Compute principal vectors from the document-term matrix X, using eigenvectors of XᵀX or its covariance matrix. section 4.6.2
Use the diagonal values of S as topic-importance weights, choose a cutoff, and discard lower-weight topics by removing columns of V. section 4.6.2
Project X onto the retained topic vectors to obtain document representations, then compare documents with cosine similarity in topic space. section 4.6.2

Toy document collection

A document-term matrix includes terms such as “violence,” “gun,” “America,” and “roses.” A topic vector assigns one contribution to each vocabulary term, while projecting documents into the retained topic space can reveal indirect similarities. section 4.6.2

Table 4.1 Document matrix for the toy example dataset

	Violence	Gun	America	⋯	Roses
d₀	0	0	0	⋯	2
d₁	1	1	1	⋯	0
d₂	2	2	0	⋯	0
d₃	3	3	0	⋯	0
d₄	5	5	0	⋯	0
d₅	0	1	0	⋯	0
d₆	1	0	0	⋯	0

Inspect the toy document matrix to see how term counts provide the input from which topic vectors are derived. section 4.6.2

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Natural Language Processing in Action, Second EditionA topic vector is a numerical representation whose components encode the strength or proportion of topics associated with a document.

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Related concepts

latent Dirichlet allocationproduced by · Latent Dirichlet allocation is a generative probabilistic topic model representing documents as mixtures of latent topics and topics as distributions over words.
term frequency-inverse document frequencyproduced by · Term frequency-inverse document frequency is a text-weighting scheme that combines a term’s frequency in a document with its inverse frequency across a document collection.
vectorkind of · A vector is an ordered, indexed sequence of elements, often numerical, represented as a mathematical quantity or a computational collection.
cosine distancemeasured by · Cosine distance is a measure of dissimilarity between nonzero vectors based on their angular separation, commonly defined as one minus cosine similarity.
latent semantic analysisproduced by · Latent semantic analysis is a dimensionality-reduction technique that factorizes term-document statistics to represent words and documents in a lower-dimensional semantic space.
similarity searchuses · Similarity search is a retrieval technique that finds or ranks items by comparing their representations with a query according to a similarity or distance measure.

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.