Related papers: On Soft Power Diagrams
In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…
Clustering and outlier detection are two important tasks in data mining. Outliers frequently interfere with clustering algorithms to determine the similarity between objects, resulting in unreliable clustering results. Currently, only a few…
Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover…
Clustering analysis is one of the critical tasks in machine learning. Traditionally, clustering has been an independent task, separate from outlier detection. Due to the fact that the performance of clustering can be significantly eroded by…
Nowadays, the use of soft computational techniques in power systems under the umbrella of machine learning is increasing with good reception. In this paper, we first present a deep learning approach to find the optimal configuration for…
We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic…
One of the methodologies that carry out the division of the electrical grid into zones is based on the aggregation of nodes characterized by similar Power Transfer Distribution Factors (PTDFs). Here, we point out that satisfactory…
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…
Cluster algorithms are increasingly popular in biomedical research due to their compelling ability to identify discrete subgroups in data, and their increasing accessibility in mainstream software. While guidelines exist for algorithm…
We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are noisy…
Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The…
Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices…
Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The…
High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
This paper introduces a novel family of outlier detection algorithms based on Cluster Catch Digraphs (CCDs), specifically tailored to address the challenges of high dimensionality and varying cluster shapes, which deteriorate the…
Rate-distortion theory-based outlier detection builds upon the rationale that a good data compression will encode outliers with unique symbols. Based on this rationale, we propose Cluster Purging, which is an extension of clustering-based…