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In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…

Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In…

Many machine learning classification systems lack competency awareness. Specifically, many systems lack the ability to identify when outliers (e.g., samples that are distinct from and not represented in the training data distribution) are…

With predictive models becoming prevalent, companies are expanding the types of data they gather. As a result, the collected datasets consist not only of simple numerical features but also more complex objects such as time series, images,…

This paper is concerned with dynamic system state estimation based on a series of noisy measurement with the presence of outliers. An incremental learning assisted particle filtering (ILAPF) method is presented, which can learn the value…

Outlying observations, which significantly deviate from other measurements, may distort the conclusions of data analysis. Therefore, identifying outliers is one of the important problems that should be solved to obtain reliable results.…

For a given set of points in a metric space and an integer $k$, we seek to partition the given points into $k$ clusters. For each computed cluster, one typically defines one point as the center of the cluster. A natural objective is to…

This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…

The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper,…

Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…

We present an Integer Linear Programming based approach to finding the optimal fusion strategy for combinator-based parallel programs. While combinator-based languages or libraries provide a convenient interface for programming parallel…

One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017, Vol. 60, p. 752-762) clusters objects based on their incidence in a large number of given sets. The idea is to minimize the occurrence of multiple objects from the…

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The…

This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference…

This paper explores a new outlier detection algorithm based on the spectrum of the Laplacian matrix of a graph. Taking advantage of boosting together with sparse-data based learners. The sparcity of the Laplacian matrix significantly…

Outlier detection (OD) is the task of identifying unusual observations (or outliers) from a given or upcoming data by learning unique patterns of normal observations (or inliers). Recently, a study introduced a powerful unsupervised OD…