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Kai Ming Ting, Jonathan R. Wells, Ye Zhu

Measuring similarity between two objects is the core operation in existing cluster analyses in grouping similar objects into clusters. Cluster analyses have been applied to a number of applications, including image segmentation, social network analysis, and computational biology. This paper introduces a new similarity measure called point-set kernel which computes the similarity between an object and a sample of objects generated from an unknown distribution. The proposed clustering procedure utilizes this new measure to characterize both the typical point of every cluster and the cluster grown from the typical point. We show that the new clustering procedure is both effective and efficient such that it can deal with large scale datasets. In contrast, existing clustering algorithms are either efficient or effective; and even efficient ones have difficulty dealing with large scale datasets without special hardware. We show that the proposed algorithm is more effective and runs orders of magnitude faster than the state-of-the-art density-peak clustering and scalable kernel k-means clustering when applying to datasets of millions of data points, on commonly used computing machines.

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Kai Ming Ting, Jonathan R. Wells, Takashi Washio

Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. To achieve this aim, the method must be able to deal with a potentially infinite number of support vectors. The current state-of-the-art is unable to deal with even a moderate number of support vectors. This paper identifies the root cause of the current methods, i.e., the type of kernel used which has a feature map of infinite dimensionality. With this revelation and together with our discovery that a recently introduced Isolation Kernel has a finite feature map, to achieve the above aim of large scale online kernel learning becomes extremely simple---simply use Isolation Kernel instead of kernels having infinite feature map. We show for the first time that online kernel learning is able to deal with a potentially infinite number of support vectors.

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Xiaoyu Qin, Kai Ming Ting, Ye Zhu, Vincent CS Lee

A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a nearest neighbour method instead. We formally prove the characteristic of Isolation Similarity with the use of the proposed method. The impact of Isolation Similarity on density-based clustering is studied here. We show for the first time that the clustering performance of the classic density-based clustering algorithm DBSCAN can be significantly uplifted to surpass that of the recent density-peak clustering algorithm DP. This is achieved by simply replacing the distance measure with the proposed nearest-neighbour-induced Isolation Similarity in DBSCAN, leaving the rest of the procedure unchanged. A new type of clusters called mass-connected clusters is formally defined. We show that DBSCAN, which detects density-connected clusters, becomes one which detects mass-connected clusters, when the distance measure is replaced with the proposed similarity. We also provide the condition under which mass-connected clusters can be detected, while density-connected clusters cannot.

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Ye Zhu, Kai Ming Ting

We identify a fundamental issue in the popular Stochastic Neighbour Embedding (SNE and t-SNE), i.e., the "learned" similarity of any two points in high-dimensional space is not defined and cannot be computed. It underlines two previously unexplored issues in the algorithm which have undermined the quality of its final visualisation output and its ability to process large datasets. The issues are:(a) the reference probability in high-dimensional space is set based on entropy which has undefined relation with local density; and (b) the use of data independent kernel which leads to the need to determine n bandwidths for a dataset of n points. This paper establishes a principle to set the reference probability via a data-dependent kernel which has a well-defined kernel characteristic that linked directly to local density. A solution based on a recent data-dependent kernel called Isolation Kernel addresses the fundamental issue as well as its two ensuing issues. As a result, it significantly improves the quality of the final visualisation output and removes one obstacle that prevents t-SNE from processing large datasets. The solution is extremely simple, i.e., simply replacing the existing data independent kernel with Isolation Kernel, leaving the rest of the t-SNE procedure unchanged.

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Ye Zhu, Kai Ming Ting, Yuan Jin, Maia Angelova

This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods to yield a density-based hierarchical clustering algorithm. Our investigation begins with formally defining the types of clusters DP and DBSCAN are designed to detect; and then identifies the kinds of distributions that DP and DBSCAN individually fail to detect all clusters in a dataset. These identified weaknesses inspire us to formally define a new kind of clusters and propose a new method called DC-HDP to overcome these weaknesses to identify clusters with arbitrary shapes and varied densities. In addition, the new method produces a richer clustering result in terms of hierarchy or dendrogram for better cluster structures understanding. Our empirical evaluation results show that DC-HDP produces the best clustering results on 14 datasets in comparison with 7 state-of-the-art clustering algorithms.

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Jonathan R. Wells, Kai Ming Ting

This paper introduces a simple and efficient density estimator that enables fast systematic search. To show its advantage over commonly used kernel density estimator, we apply it to outlying aspects mining. Outlying aspects mining discovers feature subsets (or subspaces) that describe how a query stand out from a given dataset. The task demands a systematic search of subspaces. We identify that existing outlying aspects miners are restricted to datasets with small data size and dimensions because they employ kernel density estimator, which is computationally expensive, for subspace assessments. We show that a recent outlying aspects miner can run orders of magnitude faster by simply replacing its density estimator with the proposed density estimator, enabling it to deal with large datasets with thousands of dimensions that would otherwise be impossible.

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Xin Mu, Kai Ming Ting, Zhi-Hua Zhou

This paper investigates an important problem in stream mining, i.e., classification under streaming emerging new classes or SENC. The common approach is to treat it as a classification problem and solve it using either a supervised learner or a semi-supervised learner. We propose an alternative approach by using unsupervised learning as the basis to solve this problem. The SENC problem can be decomposed into three sub problems: detecting emerging new classes, classifying for known classes, and updating models to enable classification of instances of the new class and detection of more emerging new classes. The proposed method employs completely random trees which have been shown to work well in unsupervised learning and supervised learning independently in the literature. This is the first time, as far as we know, that completely random trees are used as a single common core to solve all three sub problems: unsupervised learning, supervised learning and model update in data streams. We show that the proposed unsupervised-learning-focused method often achieves significantly better outcomes than existing classification-focused methods.

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