A heuristic approach to effective and efficient clustering on uncertain objects

We study the problem of clustering uncertain objects whose locations are uncertain and described by probability density functions (pdf). We analyze existing pruning algorithms and experimentally show that there exists a new bottleneck in the performance due to the overhead of pruning candidate clusters for assignment of each uncertain object in each iteration. In this article, we will show that by considering squared Euclidean distance, UK-means (without pruning techniques) is reduced to K-means and performs much faster than pruning algorithms, however, with some discrepancies in the clustering results due to using different distance functions. Thus, we propose Approximate UK-means to heuristically identify objects of boundary cases and reassign them to better clusters. Three models for the representation of cluster representative (certain model, uncertain model and heuristic model) are proposed to calculate expected squared Euclidean distance between objects and cluster representatives in this paper. Our experimental results show that on average the execution time of Approximate UK-means is only 25% more than K-means and our approach reduces the discrepancies of K-means' clustering results by up to 70%. While there has been a large amount of research on mining and queries on relational databases [1], the focus has been on databases that store data in exact values. In many real-life applications , however, the raw data (for example, in the case of sensor data) are not precise or accurate when they were collected or produced. The clustering of such ''uncertain'' data can be illustrated by the following simple realistic example. Considering sensors on wild animals that update their locations periodically, the sample locations of an animal over a period generate a (discrete) probability distribution function (PDF) describing the possible locations of the animal. Clustering results on those animals may reveal the possible groups and interactions between them. In our work, we consider the problem of clustering objects with multidimensional uncertainty where an object is represented by an uncertain region over which a discrete probability distribution function (PDF) or a probability density function (pdf) is defined.