EE 4780. Pattern Classification. Classification Example. Goal : Automatically classify incoming fish according to species, and send to respective packing plants. Features : Length, width, color, brightness, etc.
Goal: Automatically classify incoming fish according to species, and send to respective packing plants.
Features: Length, width, color, brightness, etc.
Model: Sea bass have some typical length, and it is greater than that for salmon.
Classifier: If the fish is longer than a value, l*, classify it as sea bass.
Training Samples: To choose l*, make length measurements from training samples and inspect the results.
Now, we have two features two classify the fish: the lightness x1, and the width x2.
Feature vector:x=[x1 x2]’.
The feature extractor reduces the image of a fish to a feature vectorx in a 2D feature space.
Question: How can we achieve rotation invariance?
x’y = x1 y1 + x2 y2 ….., xd yd = S xkyk
|| x || = sqrt( x' x )
Example: Let m1=[4.3 1.3]’ and m2=[1.5 0.3]’. Find the decision boundary.
= -2 [m’ x - .5 mk’ mk ]+x’ x
g(x) = m’ x - .5 ||mk||2
mdMin Euclidean distance Classifier
g1(x), g2(x), ... , gc(x)
and assigning x to the class corresponding to the maximum discriminant function.
x1 - m1j
x2 - m2j
xd - mdj
[ x(1,i) - m(i) ] [ x(1,i) - m(i) ] + ... + [ x(n,i) - m(i) ] [ x(n,i) - m(i) ]
[ x(1,i) - m(i) ] [ x(1,j) - m(j) ] + ... + [ x(n,i) - m(i) ] [ x(n,j) - m(j) ]
Decide w1 if P(w1) > P(w2); otherwise decide w2
Decide w1 if P(w1 | x) > P(w2 | x); otherwise decide w2
Center of the cluster is determined by the mean vector, and the shape of the cluster is determined by the covariance matrix.
“Mahalonobis distance” from x to mean.
As the priors change, the decision boundaries shift.
Solve for x from
space (here N = 2)
(here d = 1)
U. of Delaware
where ak is a scalar and e is a unit vector.
Find e that maximizes
we select the eigenvector corresponding to the largest eigenvalue.
Find the eigenvectors e1, e2, …, edcorresponding to d largest
eigenvalues of S.