quick look at machine learning happens if we turn the feature into binary featurewith value of if the animal is legless and otherwise this looks lot more plausible of courseit is not always convenient to use only binary features in section we will present more general approach to dealing with differences in scale among features clustering clustering can be defined as the process of organizing objects into groups whose members are similar in some way key issue is defining the meaning of "similar consider the plot on the rightwhich shows the heightweightand whether or not they are wearing striped shirt for people if we want to cluster people by heightthere are two obvious clusters--delimited by the dotted horizontal line if we want to cluster people by weight there are two different obvious clusters--delimited by the solid vertical line if we want to cluster people based on their shirtthere is yet third clustering--delimited by the angled dotted arrows noticeby the waythat this last division is not lineari we cannot separate the people wearing striped shirts from the others using single straight line clustering is an optimization problem the goal is to find set of clusters that optimizes an objective functionsubject to some set of constraints given distance metric that can be used to decide how close two examples are to each otherwe need to define an objective function that minimizes the distance between examples in the same clustersi minimizes the dissimilarity of the examples within cluster as we will see laterthe exact definition of the objective function can greatly influence the outcome good measure of how close the examples within single clustercare to each other is variance to compute the variance of the examples within clusterwe