Clustering on uncertain data, one of the essential tasks in mining uncertain data, posts significant challenges on both modeling similarity between uncertain objects and developing efficient computational methods. The previous methods extend traditional partitioning clustering methods like $(k)$-means and density-based clustering methods like DBSCAN to uncertain data, thus rely on geometric distances between objects. Such methods cannot handle uncertain objects that are geometrically indistinguishable, such as products with the same mean but very different variances in customer ratings. Surprisingly, probability distributions, which are essential characteristics of uncertain objects, have not been considered in measuring similarity between uncertain objects. In this paper, we systematically model uncertain objects in both continuous and discrete domains, where an uncertain object is modeled as a continuous and discrete random variable, respectively. We use the well-known Kullback-Leibler divergence to measure similarity between uncertain objects in both the continuous and discrete cases, and integrate it into partitioning and density-based clustering methods to cluster uncertain objects. Nevertheless, a naïve implementation is very costly. Particularly, computing exact KL divergence in the continuous case is very costly or even infeasible. To tackle the problem, we estimate KL divergence in the continuous case by kernel density estimation and employ the fast Gauss transform technique to further speed up the computation. Our extensive experiment results verify the effectiveness, efficiency, and scalability of our approaches.

This paper studies the problem of outlier detection on uncertain data. We start with a comprehensive model considering both uncertain objects and their instances. An uncertain object has some inherent attributes and consists of a set of instances which are modeled by a probability density distribution. We detect outliers at both the instance level and the object level. To detect outlier instances, it is a prerequisite to know normal instances. By assuming that uncertain objects with similar properties tend to have similar instances, we learn the normal instances for each uncertain object using the instances of objects with similar properties. Consequently, outlier instances can be detected by comparing against normal ones. Furthermore, we can detect outlier objects most of whose instances are outliers. Technically, we use a Bayesian inference algorithm to solve the problem, and develop an approximation algorithm and a filtering algorithm to speed up the computation. An extensive empirical study on both real data and synthetic data verifies the effectiveness and efficiency of our algorithms.

Recently, privacy preserving data publishing has received a lot of attention in both research and applications. Most of the previous studies, however, focus on static data sets. In this paper, we study an emerging problem of continuous privacy preserving publishing of data streams which cannot be solved by any straightforward extensions of the existing privacy preserving publishing methods on static data. To tackle the problem, we develop a novel approach which considers both the distribution of the data entries to be published and the statistical distribution of the data stream. An extensive performance study using both real data sets and synthetic data sets verifies the effectiveness and the efficiency of our methods.

In many applications, we need to analyze a large number of time series. Segments of time series demonstrating dominating advantages over others are often of particular interest. In this paper, we advocate interval skyline queries, a novel type of time series analysis queries. For a set of time series and a given time interval [i : j], an interval skyline query returns the time series which are not dominated by any other time series in the interval. We illustrate the usefulness of interval skyline queries in applications. Moreover, we develop an on-the-fly method and a view-materialization method to online answer interval skyline queries on time series. The on-the-fly method keeps the minimum and the maximum values of the time series using radix priority search trees and sketches, and computes the skyline at the query time. The view-materialization method maintains the skylines over all intervals in a compact data structure. Through theoretical analysis and extensive experiments, we show that both methods only require linear space and are efficient in query answering as well as incremental maintenance.

Mining user preferences plays a critical role in many important applications such as customer relationship management (CRM), product and service recommendation, and marketing campaigns. In this paper, we identify an interesting and practical problem of mining user preferences: in a multidimensional space where the user preferences on some categorical attributes are unknown, from some superior and inferior examples provided by a user, can we learn about the user's preferences on those categorical attributes? We model the problem systematically and show that mining user preferences from superior and inferior examples is challenging. Although the problem has great potential in practice, to the best of our knowledge, it has not been explored systematically before. As the first attempt to tackle the problem, we propose a greedy method and show that our method is practical using real data sets and synthetic data sets.