The Geometry of Learning
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Latent Semantic Analysis (LSA) is a mathematical technique for computationally modeling the meaning of words and larger units of texts. LSA works by applying a mathematical technique called Singular ...
Latent Semantic Analysis (LSA) is a mathematical technique for computationally modeling the meaning of words and larger units of texts. LSA works by applying a mathematical technique called Singular Value Decomposition (SVD) to a term*document matrix containing frequency counts for all words found in the corpus in all of the documents or passages in the corpus. After this SVD application, the meaning of a word is represented as a vector in a multidimensional semantic space, which makes it possible to compare word meanings, for instance by computing the cosine between two word vectors.
LSA has been successfully used in a large variety of language related applications from automatic grading of student essays to predicting click trails in website navigation. In Coh-Metrix (Graesser et al. 2004), a computational tool that produces indices of the linguistic and discourse representations of a text, LSA was used as a measure of text cohesion by assuming that cohesion increases as a function of higher cosine scores between adjacent sentences.
Besides being interesting as a technique for building programs that need to deal with semantics, LSA is also interesting as a model of human cognition. LSA can match human performance on word association tasks and vocabulary test. In this talk, Fridolin will focus on LSA as a tool in modeling language acquisition. After framing the area of the talk with sketching the key concepts learning, information, and competence acquisition, and after outlining presuppositions, an introduction into meaningful interaction analysis (MIA) is given. MIA is a means to inspect learning with the support of language analysis that is geometrical in nature. MIA is a fusion of latent semantic analysis (LSA) combined with network analysis (NA/SNA). LSA, NA/SNA, and MIA are illustrated by several examples.
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