========================================================= feature distinguisible aspect, quality, characteristic which object has example of feature: color, symbol, height/width/weight, ... ========================================================= How to mathematically express features To mathematically express features, you need : 1. feature vector : standard : column vector 2018-06-09 09-03-12.png 3 features -> 3-D column vector 3-D vector is one point in 3-D space 2018-06-09 09-03-41.png 1. feature space Space where feature vector is defined 2018-06-09 09-04-27.png 1. scatter plot You express objects in collected dots in feature space 2-D scatter plot 2018-06-09 09-07-38.png there are 2 features class has 3 objects are many ========================================================= What's pattern? set of features which each object has In task of classification, pattern is given in form of pair like $(x,\omega)$ x : feature vector $\omega$ : label of x, information about x is involved in specific class ========================================================= feature collection of features -> pattern You recognize object with pattern ========================================================= good features 2018-06-09 09-20-29.png bad features 2018-06-09 09-20-40.png In other words, sample from same class should have same or similar feature values sample from different class should have different feature values ========================================================= Type of patterm 1. pattern which can be divided by linear separation 2018-06-09 09-21-34.png 1. pattern which can be divided by non-linear separation 2018-06-09 09-21-54.png 1. pattern which has strong correlation 2018-06-09 09-22-20.png 1. pattern which has multimodal feature 2018-06-09 09-22-52.png