PatReco: Detection Alexandros Potamianos Dept of ECE, Tech. Univ. of Crete Fall

Detection  Classification problems with two classes are sometimes referred to as detection problems  For detection problems the two classes are referred to as ω 2 and ω 1 = NOT ω 2  In statistics NOT ω 2 is the null hypothesis H 0 and ω 2 is H 1

Detection  Goal: Detect an Event Hit (Success): event occurs and is detected False Alarm: event does not occur but is detected Miss (Failure): event occurs and goes undetected Correct Reject: event neither occurs nor detected  In traditional Bayes classifier terms: P(correct) = P(Hit) + P(Correct Reject) P(error) = P(False Alarm) + P (Miss)

Detection Examples  House Alarm (detect burglary)  Reading bits of a CD or a DVD (detect 1’s)  Medical screening (e.g., detect cancer) Hit (Success): cancer present and detected False Alarm: caner not present but not detected Miss (Failure): cancer present and goes undetected Correct Reject: cancer neither present nor detected Further testing No action

HitMiss False Alarm Correct Reject

Receiver Operator Curve (ROC-curve) Equal Error Rate(EER) Operation Point

Conclusions  Detection is a special case of two-class classification  Type I and Type II errors (miss and false alarms) often have different costs  Often increase Bayes error to minimize total cost  Select an operation point on the ROC-curve