A partial order framework for incomplete data clustering

We propose in this paper a partial order framework for clustering incomplete data. The paramount feature of this framework is that it spans over a partial order that can be leveraged to establish data similarity. We present the underlying theoretical foundations and study the convergence of clustering algorithms in this framework. In addition, we present a partial order-based clustering algorithm (POK-means) that illustrates the embedding of K-means clustering algorithm in our framework. The first contribution of our method is that unlike methods based on imputation of the missing values, our method does not make any assumptions about missing data. Another important contribution is that it alleviates false dismissals caused by other interval-based similarity measures. The experimental results show that, although our method do not assume any prior knowledge of (or assumptions about) missing data, it is competitive to most of published incomplete data clustering methods that are based on assumptions about input data or imputation (e.g. methods based on partial or interval kernel distances) in accuracy and performance.