1. Distance/Similarity Functions for Pattern Recognition J.-S. Roger Jang ( 張智星 ) CS Dept., Tsing Hua Univ., Taiwan http://mirlab.org/jangjang@mirlab.org 2002 音訊處理與辨識

2. 2 Distance/Similarity Functions Objects with same feature dimension L-p norms Cos similarity Mahalanobis distance … Objects with different feature dimensions Dynamic time warping Linear scaling Edit distance (for string matching) Longest common subsequence (for string matching) … 2016/3/11 2

3. 2002 音訊處理與辨識 3 2016/3/11 3 L-p Norms L-p norms (aka Minkowski distance): p = 1: City block distance, Manhattan metric, taxicab distance p = 2: Euclidean distance p = inf: maximum distance metric

4. 2002 音訊處理與辨識 4 Dynamic Time Warping (DTW) DTW is a flexible way of matching elements to compute distance between two vectors of different length Applications DTW for melody recognition DTW for speech recognition 2016/3/11 4

5. 2002 音訊處理與辨識 5 Edit distance Example: 2016/3/11 5

6. 2002 音訊處理與辨識 6 LCS (Longest Common Subsequence) Example: 2016/3/11 6