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Review of Statistical Pattern Recognition
Wen-Hung Liao 9/22/2009
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Review Paper A.K. Jain, R.P.W. Duin and J. Mao, “Statistical Pattern Recognition: A Review”, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), Vol. 22, No. 1, pp. 4-37, Jan More review papers:
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Statistical Approach in PR
Each pattern is represented in terms of d features and is viewed as a point in a d-dimensional feature space. Goal: establish decision boundaries to separate patterns belonging to different classes. Need to specify/estimate the probability distributions of the patterns.
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Various Approaches in Statistical PR
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Links Between Statistical and Neural Network Methods
Linear Discriminant Function Principal Component Analysis Nonlinear Discriminant Function Parzen Window Density-based Classifier Perceptron Auto-Associative Networks Multilayer Perceptron Radial Basis Function Network
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Model for Statistical Pattern Recognition
Classification Feature Measurement Classification Preprocessing Training Feature Extraction /Selection Learning Preprocessing
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The Curse of Dimensionality
The performance of a classifier depends on the relationship between sample sizes, number of features and classifier complexity. Number of training data points be an exponential function of the feature dimension space.
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Class-Conditional Probability
Length d feature vector: x = (x1,x2,…,xd) C Classes (or categories): w1,w2,…,wc Class-conditional probability: The probability of x happening given that it belongs to class wi: p(x|wi)
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How Many Features are Enough?
Question: More features, better classification? Answer: Yes, if the class-conditional densities are completely known. No, if we need to estimate the the class-conditional densities.
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Dimensionality Reduction
Keep the number of features as small as possible (but not too small) due to: measurement cost classification accuracy Always some trade-off
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Feature Extraction/Selection
Feature Extraction: extract features from the sensed data Feature Selection: select (hopefully) the best subset of the input feature set. Feature extraction usually precedes selection Application-domain dependent
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Example: Chernoff Faces
Three classes of face Feature set: Nose length, mouth curvature, eye size, face shape. 150 4-d patterns, 50 patterns per class.
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Chernoff Faces
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