Related papers: Dimension Reduction of Two-Dimensional Persistence…

We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the…

How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…

Frameshift mutations in protein-coding DNA sequences produce a drastic change in the resulting protein sequence, which prevents classic protein alignment methods from revealing the proteins' common origin. Moreover, when a large number of…

We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…

In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra's classical reformulation…

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…

We show an analog to the Fast Johnson-Lindenstrauss Transform for Nearest Neighbor Preserving Embeddings in $\ell_2$. These are sparse, randomized embeddings that preserve the (approximate) nearest neighbors. The dimensionality of the…

In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in…

Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time-dependent multivariate datasets. There are, however, few studies and proposals that leverage on…

We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…

Dynamic MR image reconstruction from incomplete k-space data has generated great research interest due to its capability in reducing scan time. Nevertheless, the reconstruction problem is still challenging due to its ill-posed nature. Most…

Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…

This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…

The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based on finite-dimensional models. We argue, that formally, such…

Extreme deformations of the DNA double helix attracted a lot of attention during the past decades. Particularly, the determination of the persistence length of DNA with extreme local disruptions, or kinks, has become a crucial problem in…

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…

The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…