By Neil C. Rowe

Man made Intelligence via Prolog publication

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8 Inter-textual distance by semantic similarity Using corpora or large document collections, pairs of words can be assumed to be semantically similar if they consistently tend to appear in the same parts of the text. This may be the same paragraph, or within a predetermined span or “window” (such as 10 words) of each other. One such measure of term co-occurrence is Pointwise Mutual Information. To calculate this, Turney (2001) suggested using a 10-word span. Counts are collected over very large corpora, and p (w1, w2) is the probability of seeing both word w1 and w2 in the same span of words.

Matrices can be multiplied by single values, where every element of the matrix is multiplied by that same value. 4 Similarly, a matrix can be divided by a single value, as in the example below: ( A matrix may be multiplied by a vector, provided the number of rows in the vector is the same as the number of columns in the matrix. If we just take columns 2, 3 and 4 of the final league table, which show the number of wins, draws and losses for each team, and multiply by the vector showing the number of points awarded for each type of result, we obtain the number of points awarded to each team, as shown below: Chapter 1.

PCA was developed independently by Pearson (1901) and Hotelling (1933), who gave it its name. 2 Matrix algebra To illustrate many of the facts we need to know about matrix algebra for an understanding of Paul Kline’s method of extracting principal components, consider Table 16, which is the league table from one of the group stages of the 2013 African under-17 football championship: Table 16. Matrix of football results Nigeria Ivory Coast Ghana Congo Played Won Drawn Lost Goals for Goals against Points 3 3 3 3 2 1 0 0 0 2 2 2 1 0 1 1 13 2 2 2 2 1 7 9 6 5 2 2 35 36 Literary Detective Work on the Computer A matrix is a rectangular array of numbers.