# Can cluster analysis of preclassified items gives idea about the classification performance?

Suppose in a classification we have a dataset with many features and their class, we want to select some features using which we can construct a classifier.

We perform the cluster evaluation for the given dataset taking different features (or derived features) and find cluster purity and entropy.

Can these purity and entropy calculated for certain feature vector be used to predict the classification performance of the classifier constructed for those set of features.

For eg.

I have set of features vector {A,B,C,D,E,F} and n no dataset. on selection of features there are many possible feature vectors I am considering two: X = {A,B,C,D} and Y = {A,E,F}. Now I perform cluster evaluation and find cluster purity for both X and Y. Can these purity(X) and purity(Y) predict which one is a better selection of feature for classification.

I think this purity may be a lower bound for the performance of classification.

PS: The clustering used is assumed to be k-means clustering with k = no of classes.

• You ought to define/explain purity and entropy in the question - the criterions assessing the quality or success of the clustering partition for you. – ttnphns May 20 '16 at 7:47
• Entropy: The degree to which each cluster consists of objects of a single class.Purity: Another measure of the extent to which a cluster contains objects of a single class. Their detailed mathematical formulation could be found in text www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf on page no 63 of the pdf – Shaleen Jain May 23 '16 at 9:04
• I have an experimental proof with my data set, but not sure that whether these results holds good for all. – Shaleen Jain May 26 '16 at 4:16