Outlier detection, which is the process of identifying extreme values in data, has many applications across a wide variety of industries including finance, insurance, cybersecurity and healthcare. In finance, for example, it can detect malicious events like credit card fraud. In insurance, it can identify forged or fabricated documents. In cybersecurity, it is used for identifying malicious behaviors like password theft and phishing. Finally, outlier detection has been used for rare disease detection in a healthcare context.

Analyzing numerous or long time series is difficult in practice due to the high storage costs and computational requirements. Therefore, techniques have been proposed to generate compact similarity-preserving representations of time series, enabling real-time similarity search on large in-memory data collections. However, the existing techniques are not ideally suited for assessing similarity when sequences are locally out of phase. In this paper, we propose the use of product quantization for efficient similarity-based comparison of time series under time warping. The idea is to first compress the data by partitioning the time series into equal length sub-sequences which are represented by a short code. The distance between two time series can then be efficiently approximated by pre-computed elastic distances between their codes. The partitioning into sub-sequences forces unwanted alignments, which we address with a pre-alignment step using the maximal overlap discrete wavelet transform (MODWT). To demonstrate the efficiency and accuracy of our method, we perform an extensive experimental evaluation on benchmark datasets in nearest neighbors classification and clustering applications. Overall, the proposed solution emerges as a highly efficient (both in terms of memory usage and computation time) replacement for elastic measures in time series applications.

A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the resulting tree, which is perhaps surprising considering how the explainability of a decision tree depends on these depths. To fill this gap in the literature, we propose an efficient algorithm that takes into account these metrics. In experiments on 16 datasets, our algorithm yields better results than decision-tree clustering algorithms such as the ones presented in \cite{dasgupta2020explainable}, \cite{frost2020exkmc}, \cite{laber2021price} and \cite{DBLP:conf/icml/MakarychevS21}, typically achieving lower or equivalent costs with considerably shallower trees. We also show, through a simple adaptation of existing techniques, that the problem of building explainable partitions induced by binary trees for the $k$-means cost function does not admit an $(1+\epsilon)$-approximation in polynomial time unless $P=NP$, which justifies the quest for approximation algorithms and/or heuristics.

Multiview clustering has been extensively studied to take advantage of multi-source information to improve the clustering performance. In general, most of the existing works typically compute an n * n affinity graph by some similarity/distance metrics (e.g. the Euclidean distance) or learned representations, and explore the pairwise correlations across views. But unfortunately, a quadratic or even cubic complexity is often needed, bringing about difficulty in clustering largescale datasets. Some efforts have been made recently to capture data distribution in multiple views by selecting view-wise anchor representations with k-means, or by direct matrix factorization on the original observations. Despite the significant success, few of them have considered the view-insufficiency issue, implicitly holding the assumption that each individual view is sufficient to recover the cluster structure. Moreover, the latent integral space as well as the shared cluster structure from multiple insufficient views is not able to be simultaneously discovered. In view of this, we propose an Adaptively-weighted Integral Space for Fast Multiview Clustering (AIMC) with nearly linear complexity. Specifically, view generation models are designed to reconstruct the view observations from the latent integral space with diverse adaptive contributions. Meanwhile, a centroid representation with orthogonality constraint and cluster partition are seamlessly constructed to approximate the latent integral space. An alternate minimizing algorithm is developed to solve the optimization problem, which is proved to have linear time complexity w.r.t. the sample size. Extensive experiments conducted on several realworld datasets confirm the superiority of the proposed AIMC method compared with the state-of-the-art methods.

In the Correlation Clustering problem, we are given a set of objects with pairwise similarity information. Our aim is to partition these objects into clusters that match this information as closely as possible. More specifically, the pairwise information is given as a weighted graph $G$ with its edges labelled as ``similar" or ``dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of ``disagreements": the sum of the weights of similar edges across clusters and dissimilar edges within clusters. In this exposition we focus on the case when $G$ is complete and unweighted. We explore four approximation algorithms for the Correlation Clustering problem under this assumption. In particular, we describe the following algorithms: (i) the $17429-$approximation algorithm by Bansal, Blum, and Chawla, (ii) the $4-$approximation algorithm by Charikar, Guruswami, and Wirth (iii) the $3-$approximation algorithm by Ailon, Charikar, and Newman (iv) the $2.06-$approximation algorithm by Chawla, Makarychev, Schramm, and Yaroslavtsev.

Air pollution monitoring platforms play a very important role in preventing and mitigating the effects of pollution. Recent advances in the field of graph signal processing have made it possible to describe and analyze air pollution monitoring networks using graphs. One of the main applications is the reconstruction of the measured signal in a graph using a subset of sensors. Reconstructing the signal using information from sensor neighbors can help improve the quality of network data, examples are filling in missing data with correlated neighboring nodes, or correcting a drifting sensor with neighboring sensors that are more accurate. This paper compares the use of various types of graph signal reconstruction methods applied to real data sets of Spanish air pollution reference stations. The methods considered are Laplacian interpolation, graph signal processing low-pass based graph signal reconstruction, and kernel-based graph signal reconstruction, and are compared on actual air pollution data sets measuring O3, NO2, and PM10. The ability of the methods to reconstruct the signal of a pollutant is shown, as well as the computational cost of this reconstruction. The results indicate the superiority of methods based on kernel-based graph signal reconstruction, as well as the difficulties of the methods to scale in an air pollution monitoring network with a large number of low-cost sensors. However, we show that scalability can be overcome with simple methods, such as partitioning the network using a clustering algorithm.

Equal contribution *To whom correspondence should be addressed. Abstract Recent development in angle-resolved photoemission spectroscopy (ARPES) technique involves spatially resolving samples while maintaining the high-resolution feature of momentum space. This development easily expands the data size and its complexity for data analysis, where one of it is to label similar dispersion cuts and map them spatially. In this work, we demonstrate that the recent development in representational learning (self-supervised learning) model combined with k-means clustering can help automate that part of data analysis and save precious time, albeit with low performance. Finally, we introduce a few-shot learning (k-nearest neighbour or kNN) in representational space where we selectively choose one (k=1) image reference for each known label and subsequently label the rest of the data with respect to the nearest reference image. This last approach demonstrates the strength of the selfsupervised learning to automate the image analysis in ARPES in particular and can be generalized into any science data analysis that heavily involves image data.

Automatic Identification System (AIS) messages are useful for tracking vessel activity across oceans worldwide using radio links and satellite transceivers. Such data plays a significant role in tracking vessel activity and mapping mobility patterns such as those found in fishing. Accordingly, this paper proposes a geometric-driven semi-supervised approach for fishing activity detection from AIS data. Through the proposed methodology we show how to explore the information included in the messages to extract features describing the geometry of the vessel route. To this end, we leverage the unsupervised nature of cluster analysis to label the trajectory geometry highlighting the changes in the vessel's moving pattern which tends to indicate fishing activity. The labels obtained by the proposed unsupervised approach are used to detect fishing activities, which we approach as a time-series classification task. In this context, we propose a solution using recurrent neural networks on AIS data streams with roughly 87% of the overall $F$-score on the whole trajectories of 50 different unseen fishing vessels. Such results are accompanied by a broad benchmark study assessing the performance of different Recurrent Neural Network (RNN) architectures. In conclusion, this work contributes by proposing a thorough process that includes data preparation, labeling, data modeling, and model validation. Therefore, we present a novel solution for mobility pattern detection that relies upon unfolding the trajectory in time and observing their inherent geometry.

Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using linear subspaces are two most popular techniques to partition real-world data into smaller clusters. However, when the data consists of sensitive demographic groups, significantly different clustering cost per point for different sensitive groups can lead to fairness-related harms (e.g., different quality-of-service). The goal of socially fair clustering is to minimize the maximum cost of clustering per point over all groups. In this work, we propose a unified framework to solve socially fair center-based clustering and linear subspace clustering, and give practical, efficient approximation algorithms for these problems. We do extensive experiments to show that on multiple benchmark datasets our algorithms either closely match or outperform state-of-the-art baselines.

Machine learning models and algorithms have been used in a number of systems that take decisions that affect our lives. Thus, explainable methods are desirable so that people are able to have a better understanding of their behavior, which allows for comfortable use of these systems or, eventually, the questioning of their applicability [1]. Recently, there has been some effort to devise explainable methods for unsupervised learning tasks, in particular, for clustering [2, 3]. We investigate the framework discussed by [2], where an explainable clustering is given by a partition, induced by the leaves of an axis-aligned decision tree, that optimizes some predefined objective function. Figure 1 shows a decision tree that defines a clustering for the Iris dataset.