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Overview[ edit ] Animation of the topic detection process in a document-word matrix. Every column corresponds to a document, every row to a word. A cell stores the weighting of a word in a document e. LSA groups both documents that contain similar words, as well as words that occur in a similar set of documents.
The resulting patterns are used to detect latent components. A typical example of the weighting of the elements of the matrix is tf-idf term frequency—inverse document frequency: This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used.
Rank lowering[ edit ] After the construction of the occurrence matrix, LSA finds a low-rank approximation  to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation a "least and necessary evil".
The original term-document matrix is presumed noisy: From this point of view, the approximated matrix is interpreted as a de-noisified matrix a better matrix than the original. The original term-document matrix is presumed overly sparse relative to the "true" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document—generally a much larger set due to synonymy.
The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: It also mitigates the problem with polysemysince components of polysemous words that point in the "right" direction are added to the components of words that share a similar meaning.
Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense.Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and caninariojana.com assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis).
Relearning the learning curve: a review of the derivation and applications of learning curve theory. Project Management Journal, 31 (1), 24– Reprints and Permissions. The basic discounting formula and tables are all that is needed to derive useful measures of project worth.
However, in some cases other formulas - derived from the above basic formula - can provide useful shortcuts in carrying out calculations.
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