Related papers: Dimensionality Reduction Using pseudo-Boolean poly…

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…

In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…

In this paper, we present a novel approach to synthesize invariant clusters for polynomial programs. An invariant cluster is a set of program invariants that share a common structure, which could, for example, be used to save the needs for…

In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…

Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…

An iterative computer-aided ideation procedure is introduced, building on recent quality-diversity algorithms, which search for diverse as well as high-performing solutions. Dimensionality reduction is used to define a similarity space, in…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

Bloom filters are widely used data structures that compactly represent sets of elements. Querying a Bloom filter reveals if an element is not included in the underlying set or is included with a certain error rate. This membership testing…

One of the goals of NASA funded project at IBM T. J. Watson Research Center was to build an index for similarity searching satellite images, which were characterized by high-dimensional feature image texture vectors. Reviewed is our effort…

Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…

Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure. However, such a structure may not always appear in the projections. Existing DR quality metrics…

Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised…

We study the topic of dimensionality reduction for $k$-means clustering. Dimensionality reduction encompasses the union of two approaches: \emph{feature selection} and \emph{feature extraction}. A feature selection based algorithm for…

Standard approaches to tackle high-dimensional supervised classification problem often include variable selection and dimension reduction procedures. The novel methodology proposed in this paper combines clustering of variables and feature…

Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…

Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…

Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods…