  Many real-world clustering problems are plagued by incomplete data
characterized by missing or absent features for some or all of the data
instances. Traditional clustering methods cannot be directly applied to such
data without preprocessing by imputation or marginalization techniques. In this
article, we overcome this drawback by utilizing a penalized dissimilarity
measure which we refer to as the Feature Weighted Penalty based Dissimilarity
(FWPD). Using the FWPD measure, we modify the traditional k-means clustering
algorithm and the standard hierarchical agglomerative clustering algorithms so
as to make them directly applicable to datasets with missing features. We
present time complexity analyses for these new techniques and also undertake a
detailed theoretical analysis showing that the new FWPD based k-means algorithm
converges to a local optimum within a finite number of iterations. We also
present a detailed method for simulating random as well as feature dependent
missingness. We report extensive experiments on various benchmark datasets for
different types of missingness showing that the proposed clustering techniques
have generally better results compared to some of the most well-known
imputation methods which are commonly used to handle such incomplete data. We
append a possible extension of the proposed dissimilarity measure to the case
of absent features (where the unobserved features are known to be undefined).
