1. Machines that Make Decisions Instructor: Edmondo Trentin trentin@dii.unisi.it http://www.dii.unisi.it/~trentin

2. Decision (Classification) Problems The vending machine The vending machine Speech recognition Speech recognition Lip reading Lip reading Speaker recognition Speaker recognition Identification for security issues (fingerprint recognition, other biometrics) Identification for security issues (fingerprint recognition, other biometrics) Optical character recognition Optical character recognition Image (e.g., face) classification Image (e.g., face) classification Classifiers for biomedical (e.g., ECG) and bioinformatics (e.g., functional and structural genomics) applications Classifiers for biomedical (e.g., ECG) and bioinformatics (e.g., functional and structural genomics) applications

3. General Diagram of the System Event Extract feature Classify Class 1.In the real world an EVENT takes place (eg. An instance of an object is detected) 2.PERCEPTION: a FEATURE EXTRACTION PROCESS gives a digitalized description of the event within a proper feature space 3.ACTION: a CLASSIFICATION PROCESS decides which CLASS the event belongs to (amongst c alternative classes)

4. Relevance of the Features The difficulty of a given classification problem depends on the specific features one is able/can afford to extract (eg. gender classifier) The difficulty of a given classification problem depends on the specific features one is able/can afford to extract (eg. gender classifier) The features must be as compact (small dimensionality) and as informatively rich as possible The features must be as compact (small dimensionality) and as informatively rich as possible

5. Types of Features Numeric (discrete or continuous): number of black pixels in a bitmap, frequency of a sound, angle of orientation of a line of handwritten text, weight and measures of an item, … Numeric (discrete or continuous): number of black pixels in a bitmap, frequency of a sound, angle of orientation of a line of handwritten text, weight and measures of an item, … Symbolic: symbols or strings of symbols over a given finite and discrete alphabet (eg. text on a web-page, sequence of amino-acids,...) Symbolic: symbols or strings of symbols over a given finite and discrete alphabet (eg. text on a web-page, sequence of amino-acids,...) Qualitative: tall, short, big, small, red, blue, good, bad, normal, strange, … Qualitative: tall, short, big, small, red, blue, good, bad, normal, strange, … We will mostly use numeric features. Qualitative ones may be encoded with numerical values.

6. Feature extraction: example 1

7. Feature extraction: example 2 Waveform “Spectral” parameters

8. Discriminant Function Let us consider a c-class classification task Let us consider a c-class classification task The patterns x are d-dimensional vectors The patterns x are d-dimensional vectors For each class i, i=1,…,c, a discriminant function g(i,x) is sought such that: g(i,x)>g(j,x) iff x belongs to i-th class For each class i, i=1,…,c, a discriminant function g(i,x) is sought such that: g(i,x)>g(j,x) iff x belongs to i-th class For each new event, the classifier decides on the class the event belongs to by picking that particular class whose discriminant function has the maximum value For each new event, the classifier decides on the class the event belongs to by picking that particular class whose discriminant function has the maximum value

9. Intuitive Approach 1: Probability Distributions of the Classes

10. Intuitive Approach 2: Separation Surfaces