Classification Heejune Ahn SeoulTech Last updated May. 03

Outline Introduction  Purpose, type, and an example Classification design  Design flow  Simple classifier  Linear discriminant functions  Mahalanobis distance Bayesian classification K-means clustering : unsupervised learning

1.Pupose Purpose  For decision making  Topics of Pattern recognition (in artificial intelligence) Model Automation and Human intervention  Task specification: what classes, what features  Algorithm to used  Training: tuning algorithm parameters Classifier (classification rules) classes Features (patterns, structures) Images

2. Supervised vs unsupervised Supervised (classification)  trained by examples (by humans) Unsupervised (clustering)  only by feature data  using the mathematical properties (statistics) of data set

3. An example Classifying nuts Classifier (classification rules) Pine-nuts Lentils Pumpkin seeds Features (circularity, line-fit-error) lentil pumpkin seed pine nut

Observations  What if a single features used?  What for the singular points? Classification  draw boundaries

Terminalogy

4. Design Flow

5. Prototypes & min-distance classifier Prototypes  mean of training samples in each class

6. Linear discriminant Linear discriminant function  g(x1,x2) = a*x1 + b*x2 + c = 0   Ex 11.1 & Fig11.6

8. Mahalanobis distance Problems In min-dist.  mean-value only, no distribution considered  e.g. (right figure) std(class 1) << std(class 2) Mahalanobis dist. Variance considered. (larger variance, less distance)

9. Bayesian classification Idea  To assign each data to the “most-probable” class, based on “apriori-known probability”  Assumption Priors (probability for class) are known. Bayes theorem

10. Bayes decision rule Classification rule Bayes Theorem Intuitively Class-conditional probability density function Prior probability Total probability & Not used in classification decision

Interpretation  Need to know priors and class-conditional pdf: often not available  MVN (multivariate normal) distribution model Practically quite good approximation MVN  N-D Normal distribution with

12. Bayesian classifier for M-varirates taking log( ) It is monotonic increasing function

Case 1: identical independent Linear Machine: the decision region is hyper-plane (linears) Note: when same prob(w), then Minimum distance criterion

Case 2: all covariance is same: Matlab  [class, err] = classify(test, training, group[, type, prior]) training and test Type ‘DiagLinear’ for naïve Baysian

Ex11.3 wrong priorscorrect priors

13. Ensemble classifier Combining multiple classifiers  Utilizing diversity, similar to ask multiple experts for decision. AdaBoost  Weak classifier: change (1/2) < accuracy << 1.0  weighting mis-classified training data for next classifiers H 1 (x)D 1 (x)H 2 (x) D 2 (x) H t (x) D 2 (x) H T (x) D T (x) uniform a t (x)

AdaBoost in details  Given:  Initialize weight:  For t = 1,..., T: 1. WeakLearn, which return the weak classifier with minimum error w.r.t. distribution D t 2. Choose 3. Update Where Z t is a normalization factor chosen so that D t+1 is a distribution  Output the strong classifier:

14. K-means clustering K-means  Unsupervised classification  Group data to minimize  Iterative algorithm (re-)assign X i ’s to class (re-)calculate c i  Demo

Issues  Sensitive to “initial” centroid values. Multiple trials needed => choose the best one  ‘K’ (# of clusters) should be given. Trade-off in K (bigger) and the objective function (smaller) No optimal algorithm to determine it. Nevertheless  used in most of un-supervised clustering now.

Ex11.4 & F11.10  kmeans function  [classIndexes, centers] = kmeans(data, k, options) k : # of clusters Options: ‘Replicates', ‘Display’