In data stream clustering, it is desirable to have algorithms that are able to detect clusters of arbitrary shape, clusters that evolve over time, and clusters with noise. Existing stream data clustering algorithms are generally based on an online-offline approach: The online component captures synopsis information from the data stream (thus, overcoming real-time and memory constraints) and the offline component generates clusters using the stored synopsis. The online-offline approach affects the overall performance of stream data clustering in various ways: the ease of deriving synopsis from streaming data; the complexity of data structure for storing and managing synopsis; and the frequency at which the offline component is used to generate clusters. In this article, we propose an algorithm that (1) computes and updates synopsis information in constant time; (2) allows users to discover clusters at multiple resolutions; (3) determines the right time for users to generate clusters from the synopsis information; (4) generates clusters of higher purity than existing algorithms; and (5) determines the right threshold function for density-based clustering based on the fading model of stream data. To the best of our knowledge, no existing data stream algorithms has all of these features. Experimental results show that our algorithm is able to detect arbitrarily shaped, evolving clusters with high quality.

Exploratory data analysis aims to discover and generate multiple views of the structure within a dataset. Conventional clustering techniques, however, are designed to only provide a single grouping or clustering of a dataset. In this paper, we introduce a novel algorithm called CAMI, that can uncover alternative clusterings from a dataset. CAMI takes a mathematically appealing approach, combining the use of mutual information to distinguish between alternative clusterings, coupled with an expectation maximization framework to ensure clustering quality. We experimentally test CAMI on both synthetic and real-world datasets, comparing it against a variety of state-of-the-art algorithms. We demonstrate that CAMI's performance is high and that its formulation provides a number of advantages compared to existing techniques.

Outlier detection aims at searching for a small set of objects that are inconsistent or considerably deviating from other objects in a dataset. Existing research focuses on outlier identification while omitting the equally important problem of outlier interpretation. This paper presents a novel method named LODI to address both problems at the same time. In LODI, we develop an approach that explores the quadratic entropy to adaptively select a set of neighboring instances, and a learning method to seek an optimal subspace in which an outlier is maximally separated from its neighbors. We show that this learning task can be solved via the matrix eigen-decomposition and its solution contains essential information to reveal features that are most important to interpret the exceptional properties of outliers. We demonstrate the appealing performance of LODI via a number of synthetic and real world datasets and compare its outlier detection rates against state-of-the-art algorithms.

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Data mining practitioners are facing challenges from data with network structure. In this paper, we address a specific class of global-state networks which comprises of a set of network instances sharing a similar structure yet having different values at local nodes. Each instance is associated with a global state which indicates the occurrence of an event. The objective is to uncover a small set of discriminative subnetworks that can optimally classify global network values. Unlike most existing studies which explore an exponential subnetwork space, we address this difficult problem by adopting a space transformation approach. Specifically, we present an algorithm that optimizes a constrained dualobjective function to learn a low-dimensional subspace that is capable of discriminating networks labelled by different global states, while reconciling with common network topology sharing across instances. Our algorithm takes an appealing approach from spectral graph learning and we show that the globally optimum solution can be achieved via matrix eigen-decomposition.