Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity between an object and a set of objects. The proposed clustering procedure utilizes this new measure to characterize every cluster grown from a seed object. We show that the new clustering procedure is both effective and efficient that enables it to deal with large scale datasets. In contrast, existing clustering algorithms are either efficient or effective. In comparison with the state-of-the-art density-peak clustering and scalable kernel k-means clustering, we show that the proposed algorithm is more effective and runs orders of magnitude faster when applying to datasets of millions of data points, on a commonly used computing machine.

This paper shows that adaptive kernel density estimator (KDE) can be derived effectively from Isolation Kernel. Existing adaptive KDEs often employ a data independent kernel such as Gaussian kernel. Therefore, it requires an additional means to adapt its bandwidth locally in a given dataset. Because Isolation Kernel is a data dependent kernel which is derived directly from data, no additional adaptive operation is required. The resultant estimator called IKDE is the only KDE that is fast and adaptive. Existing KDEs are either fast but non-adaptive or adaptive but slow. In addition, using IKDE for anomaly detection, we identify two advantages of IKDE over LOF (Local Outlier Factor), contributing to significantly faster runtime.

Density estimation is the ubiquitous base modelling mechanism employed for many tasks such as clustering, classification, anomaly detection and information retrieval. Commonly used density estimation methods such as kernel density estimator and k-nearest neighbour density estimator have high time and space complexities which render them inapplicable in problems with large data size and even a moderate number of dimensions. This weakness sets the fundamental limit in existing algorithms for all these tasks. We propose the first density estimation method which stretches this fundamental limit to an extent that dealing with millions of data can now be done easily and quickly. We analyze the error of the new estimation (from the true density) using a bias-variance analysis. We then perform an empirical evaluation of the proposed method by replacing existing density estimators with the new one in two current density-based algorithms, namely, DBSCAN and LOF. The results show that the new density estimation method significantly improves the runtime of DBSCAN and LOF, while maintaining or improving their task-specific performances in clustering and anomaly detection, respectively. The new method empowers these algorithms, currently limited to small data size only, to process very large databases - setting a new benchmark for what density-based algorithms can achieve.

Mass estimation, an alternative to density estimation, has been shown recently to be an effective base modelling mechanism for three data mining tasks of regression, information retrieval and anomaly detection. This paper advances this work in two directions. First, we generalise the previously proposed one-dimensional mass estimation to multidimensional mass estimation, and significantly reduce the time complexity to O(ψh) from O(ψh)-making it feasible for a full range of generic problems. Second, we introduce the first clustering method based on mass-it is unique because it does not employ any distance or density measure. The structure of the new mass model enables different parts of a cluster to be identified and merged without expensive evaluations. The characteristics of the new clustering method are: (i) it can identify arbitrary-shape clusters; (ii) it is significantly faster than existing density-based or distance-based methods; and (iii) it is noise-tolerant.