David B. Bracewell

David B. Bracewell http://www.davidbracewell.com Information about me and my research Fri, 12 Feb 2010 19:17:57 +0000 http://wordpress.org/?v=2.9.1 en hourly 1 Pointwise Mutual Information http://www.davidbracewell.com/math/statisitics/mutual-information-for-bigrams http://www.davidbracewell.com/math/statisitics/mutual-information-for-bigrams#comments Fri, 12 Feb 2010 14:10:23 +0000 David http://www.davidbracewell.com/?p=79
$= log( p(x,y) ) - log( p(x) ) - log( p(y) )$

where…

$p(x,y) = \frac{ COUNT(X,Y) }{ N }$ ,
$p(x) = \frac{ COUNT(X) }{ N }$ ,
$p(y) = \frac{ COUNT(Y) }{ N }$
and $N= \sum_i{ COUNT(w_i)}$ .

This can simplified as…
$I(x,y) = \frac{ N \cdot COUNT(X,Y) }{ COUNT(X) \cdot COUNT(Y)}$ ]]> http://www.davidbracewell.com/math/statisitics/mutual-information-for-bigrams/feed 0 Matrix: Basic Operations http://www.davidbracewell.com/math/linear-alegbra/matrix-basic-operations http://www.davidbracewell.com/math/linear-alegbra/matrix-basic-operations#comments Fri, 12 Feb 2010 13:50:00 +0000 David http://www.davidbracewell.com/?p=69 Addition $A + B = \left| \begin{array}{ccc} a_{11} + b_{11} & \cdots & a_{1n} + b_{1n} \\ \vdots & \ddots & \vdots \\a_{m1} + b_{m1} & \cdots & a_{mn} + b_{mn} \\\end{array} \right|$

Associative Law:
$A + B + C = (A+B) + C = A + (B + C)$

Commutative Law:
$A + B = B + A$

Subtraction

$A - B = \left| \begin{array}{ccc} a_{11} - b_{11} & \cdots & a_{1n} - b_{1n} \\ \vdots & \ddots & \vdots \\a_{m1} - b_{m1} & \cdots & a_{mn} - b_{mn} \\\end{array} \right|$

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