K Means vs K - Modes

The average taken for a set of numbers is called a mean. The middle value in the data set is called the Median. 

The number that occurs the most in a given list of numbers is called a mode.

K-modes is really only applicable for categoricial data. Not for sparse numerical data like bag-of-words or tf-idf vectors.

Silhouette Method - This method measure the distance from points in one cluster to the other clusters. Then visually you have silhouette plots that let you choose K.

• K-means clustering for numerical data.
• K-prototype clustering on mixed data. (numerical + categorical data)

Handle categorical variable

• It depends on your categorical variable being used. For ordinal variables, say like bad,average and good, it makes sense just to use one variable and have values 0,1,2 

Algos List

• Partitioning-based algorithms: k-Prototypes, Squeezer
• Hierarchical algorithms: ROCK, Agglomerative single, average, and complete linkage
• Density-based algorithms: HIERDENC, MULIC, CLIQUE
• Model-based algorithms: SVM clustering, Self-organizing maps
• Cluster using e.g., k-means or DBSCAN, based on only the continuous features
• Use k-prototypes to directly cluster the mixed data
• Use FAMD (factor analysis of mixed data) to reduce the mixed data to a set of derived continuous features which can then be clustered.

The k-means algorithm is the most widely used centre based partitional clustering algorithm.

K modes changes

• using a simple matching dissimilarity measure for categorical objects,
• replacing means of clusters by modes, and
• using a frequency-based method to update the modes.

Ref - Link1, Link2

Keep Exploring!!!