Abstract Hierarchical clustering produces a cluster tree with different granularities. As a result, hierarchical clustering provides richer information and insight into a dataset than partitioning clustering. However, hierarchical clustering algorithms often have two weaknesses: scalability and the capacity to handle clusters of varying densities. This is because they rely on pairwise point-based similarity calculations and the similarity measure is independent of data distribution. In this paper, we aim to overcome these weaknesses and propose a novel efficient hierarchical clustering called StreaKHC that enables massive streaming data to be mined. The enabling factor is the use of a scalable point-set kernel to measure the similarity between an existing cluster in the cluster tree and a new point in the data stream. It also has an efficient mechanism to update the hierarchical structure so that a high-quality cluster tree can be maintained in real-time. Our extensive empirical evaluation shows that StreaKHC is more accurate and more efficient than existing hierarchical clustering algorithms.

Point Cloud Normal Estimation via Representation Learning on Height Maps

Abstract Visual Assessment of cluster Tendency (VAT) is a popular method that visually represents the possible clusters found in a dataset as dark blocks along the diagonal of a reordered dissimilarity image (RDI). Although many variants of the VAT algorithm have been proposed to improve the visualisation quality on different types of datasets, they still suffer from the challenge of extracting clusters with varied densities. In this paper, we focus on overcoming this drawback of VAT algorithms by incorporating kernel methods and also propose a novel adaptive cluster extraction strategy, named CER, to effectively identify the local clusters from the RDI. We examine their effects on an improved VAT method (iVAT) and systematically evaluate the clustering performance on 18 synthetic and real-world datasets. The experimental results reveal that the recently proposed data-dependent dissimilarity measure, namely the Isolation kernel, helps to significantly improve the RDI image for easy cluster identification. Furthermore, the proposed cluster extraction method, CER, outperforms other existing methods on most of the datasets in terms of a series of dissimilarity measures.

Trajectory clustering enables the discovery of common patterns in trajectory data. Current methods of trajectory clustering rely on a distance measure between two points in order to measure the dissimilarity between two trajectories, causing problems of both effectiveness and efficiency. In this paper, we propose a new IDK-based clustering algorithm, called TIDKC, which makes full use of the distributional kernel for trajectory similarity measuring and clustering. TIDKC identifies non-linearly separable clusters with irregular shapes and varied densities in linear time. It does not rely on random initialisation and is robust to outliers. An extensive evaluation on 7 large real-world trajectory datasets confirms that IDK is more effective in capturing complex structures in trajectories than traditional and deep learning-based distance measures.

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.

Hierarchical clustering produces a cluster tree with different granularities. As a result, hierarchical clustering provides richer information and insight into a dataset than partitioning clustering. However, hierarchical clustering algorithms often have two weaknesses: scalability and the capacity to handle clusters of varying densities. This is because they rely on pairwise point-based similarity calculations and the similarity measure is independent of data distribution. In this paper, we aim to overcome these weaknesses and propose a novel efficient hierarchical clustering called StreaKHC that enables massive streaming data to be mined. The enabling factor is the use of a scalable point-set kernel to measure the similarity between an existing cluster in the cluster tree and a new point in the data stream. It also has an efficient mechanism to update the hierarchical structure so that a high-quality cluster tree can be maintained in real-time. Our extensive empirical evaluation shows that StreaKHC is more accurate and more efficient than existing hierarchical clustering algorithms.

Time series is traditionally treated with two main approaches, i.e., the time domain approach and the frequency domain approach. These approaches must rely on a sliding window so that time-shift versions of a periodic subsequence can be measured to be similar. Coupled with the use of a root point-to-point measure, existing methods often have quadratic time complexity. We offer the third R domain approach. It begins with an insight that subsequences in a periodic time series can be treated as sets of independent and identically distributed (iid) points generated from an unknown distribution in R. This R domain treatment enables two new possibilities: (a) the similarity between two subsequences can be computed using a distributional measure such as Wasserstein distance (WD), kernel mean embedding or Isolation Distributional kernel (IDK); and (b) these distributional measures become non-sliding-window-based. Together, they offer an alternative that has more effective similarity measurements and runs significantly faster than the point-to-point and sliding-window-based measures. Our empirical evaluation shows that IDK and WD are effective distributional measures for time series; and IDK-based detectors have better detection accuracy than existing sliding-window-based detectors, and they run faster with linear time complexity.

This paper addresses reliable and efficient calculation of the mode of a multivariate sample, which is a classical fusion function. In particular, we focus on the inputs given on the unit simplex, when aggregating elements of Atanassov intuitionistic fuzzy sets, interval-valued fuzzy sets and their extensions, as well as compositional data. We outline the use of a specially designed 2-additive fuzzy measures and the Choquet integral for the purposes of reducing computational complexity in higher dimensions. We present computational analysis and benchmark four different methods of density-based mode estimation.

This paper introduces the first generic version of data dependent dissimilarity and shows that it provides a better closest match than distance measures for three existing algorithms in clustering, anomaly detection and multi-label classification. For each algorithm, we show that by simply replacing the distance measure with the data dependent dissimilarity measure, it overcomes a key weakness of the otherwise unchanged algorithm.