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Singular Value Decomposition Tutorial |
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When you browse standard web sources like Singular Value Decomposition (SVD) on Wikipedia, you find many equations, but not an intuitive explanation of what it is or how it works. Singular Value Decomposition is a way of factoring matrices into a series of linear approximations that expose the underlying structure of the matrix.
SVD is extraordinarily useful and has many applications such as data analysis, signal processing, pattern recognition, image compression, weather prediction, and Latent Semantic Analysis or LSA (also referred to as Latent Semantic Indexing or LSI).
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Latent Semantic Analysis Tutorial |
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Latent Semantic Analysis (LSA), also known as Latent Semantic Indexing (LSI) literally means analyzing documents to find the underlying meaning or concepts of those documents. If each word only meant one concept, and each concept was only described by one word, then LSA would be easy since there is a simple mapping from words to concepts.
Unfortunately, this problem is difficult because English has different words that mean the same thing (synonyms), words with multiple meanings, and all sorts of ambiguities that obscure the concepts to the point where even people can have a hard time understanding.
For example, the word bank when used together with mortgage, loans, and rates probably means a financial institution. However, the word bank when used together with lures, casting, and fish probably means a stream or river bank.
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