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Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…

Circle fitting methods are extensively utilized in various industries, particularly in quality control processes and design applications. The effectiveness of these algorithms can be significantly compromised when the point sets to be…

Invariant Coordinate Selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an…

In this paper we introduce a new method for detecting outliers in a set of proportions. It is based on the construction of a suitable two-way contingency table and on the application of an algorithm for the detection of outlying cells in…

Outlier detection is one of the most important processes taken to create good, reliable data in machine learning. The most methods of outlier detection leverage an auxiliary reconstruction task by assuming that outliers are more difficult…

Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…

Feature selection places an important role in improving the performance of outlier detection, especially for noisy data. Existing methods usually perform feature selection and outlier scoring separately, which would select feature subsets…

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

In this paper we propose a new efficient linear programming based approach for multi-resource allocation and location problems in disaster management. Such problems require an integer solution and therefore, in most cases, the computations…

Several methods have been proposed to estimate the number of clusters in a dataset; the basic ideal behind all of them has been to study an index that measures inter-cluster separation and intra-cluster cohesion over a range of cluster…

We present a new algorithm for locating a small cluster of points with differential privacy [Dwork, McSherry, Nissim, and Smith, 2006]. Our algorithm has implications to private data exploration, clustering, and removal of outliers.…

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with…

In this paper we propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n \log n)$…

As language models become more general purpose, increased attention needs to be paid to detecting out-of-distribution (OOD) instances, i.e., those not belonging to any of the distributions seen during training. Existing methods for…

We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…

Real-world applications may be affected by outlying values. In the model-based clustering literature, several methodologies have been proposed to detect units that deviate from the majority of the data (rowwise outliers) and trim them from…

Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to…