Motivation ™ Several applications have different costs associated with different classification-errors Example: intrusion detection, biometric recognition, etc. ™ Most classification systems are geared towards minimizing the error rate and not cost True objective function to be minimized is the cost of classification-error and not error-rate itself ™ Existing approaches can not handle multi-class problems or dynamically changing costs ROC curves (multi-class? [1] ) ; cost-sensitive Adaboost [2] (dynamically changing costs? ) Goal Develop a classification-error cost minimization strategy that ™ Can deal with multiple classes in a principled manner ™ Is a simple post-training step Does not require re-training of classifiers for changing costs ™ Is classifier type independent Exploits statistical properties of the trained classifier Contributions costs incurred™ Statistically significant reduction in ™ Effective on ƒ a variety of applications ƒ data sets of varying dimensionalities ƒ a variety of classifier types Approach

™ Solution for a two-class, one-feature problem, known distributions ™ If unknown distribution Estimate with a histogram ™ If multiple-features Classification system: maps multiple-features to a single score/feature ™ If multiple-classes High dimensional histogram is not feasible … so then? Intuition: Convert C-class problem to C 2-class problems We have a trained classification system Probability of a misclassified instance classified as class c actually belonging to class i: Expected cost of false positives:

(Iterate to get a new confusion matrix with new thresholds) Final classification decision: Pick the class corresponding to the score furthest away from it’s corresponding optimum threshold Results ™ Synthetic data: MLP neural network

™ MIT-DARPA intrusion detection [3] 0.3 million data points 5 classes: DenialOfService, Probe, UserToRoot, RootToLocal, Normal Ensemble of classifiers based classification system: Learn++ [4] (can perform data fusion)41 features 3 feature sets: traffic, content, intrinsic features

™ PCA reduced intrusion detection

™ Other applications [5]

References: [1] N. Lachiche and P. Flach. Improving accuracy and cost of two-class and multi-class probabilistic classifiers using ROC curves. ICML, 2003. [2] Y. Ma and X. Ding. Robust real-time face detection based on cost-sensitive AdaBoost method. ICME, 2003 [3] The UCI KDD Archive, Information and Computer Science, University of California, Irvine, http://kdd.ics.uci.edu/ databases/kddcup99/kddcup99.html [4] D. Parikh and R. Polikar. An Ensemble-Based Incremental Learning Approach to Data Fusion. In IEEE Transactions on Systems, Man and Cybernetics, 2007. [5] C. Blake and C. Merz. UCI Repository of Machine Learning Database at Irvine CA, 2005. http://mlearn.ics.uci.edu/MLRepository.html