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logp

Log unconditional probability density for discriminant analysis classifier

Description

example

lp = logp(mdl,X) returns the log of the unconditional probability density of each row of the predictor data, computed using the discriminant analysis classifier mdl.

Examples

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Construct a discriminant analysis classifier for Fisher's iris data, and examine its prediction for an average measurement.

Load Fisher's iris data and construct a default discriminant analysis classifier.

load fisheriris
Mdl = fitcdiscr(meas,species);

Find the log probability of the discriminant model applied to an average iris.

logpAverage = logp(Mdl,mean(meas))
logpAverage = -1.7254

Input Arguments

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Trained discriminant analysis classifier, specified as a ClassificationDiscriminant or CompactClassificationDiscriminant model object trained with fitcdiscr.

Predictor data to classify, specified as a matrix. Each row of the matrix represents an observation, and each column represents a predictor. The number of columns in X must equal the number of predictors in mdl.

Output Arguments

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Logarithms of unconditional probability densities, specified as a column vector with the same number of rows as X. Each entry is the logarithm of the unconditional probability density of the corresponding row of X.

More About

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Unconditional Probability Density

The unconditional probability density of a point x of a discriminant analysis model is

P(x)=k=1KP(k)P(x|k),

where P(k) is the prior probability of class k, P(x|k) is the conditional density of x given class k, and K is the total number of classes. The conditional density function of the multivariate normal with 1-by-d mean μk and d-by-d covariance Σk at a 1-by-d point x is

P(x|k)=1((2π)d|Σk|)1/2exp(12(xμk)Σk1(xμk)T),

where |Σk| is the determinant of Σk, and Σk1 is the inverse matrix.

Version History

Introduced in R2011b