相关论文: Central subspace data depth

The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

Data depth is an efficient tool for robustly summarizing the distribution of functional data and detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal…

In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…

Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…

Data cohesion, a recently introduced measure inspired by social interactions, uses distance comparisons to assess relative proximity. In this work, we provide a collection of results which can guide the development of cohesion-based methods…

We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a…

In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…

Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…

Objective-The main purpose of this paper is to construct a distributed clustering algorithm such that each distributed cluster can perform the data accuracy at their respective cluster head node before data aggregation and transmit the data…

The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…

Data matrix centering is an ever-present yet under-examined aspect of data analysis. Functional data analysis (FDA) often operates with a default of centering such that the vectors in one dimension have mean zero. We find that centering…

This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

Subspace clustering aims to find groups of similar objects (clusters) that exist in lower dimensional subspaces from a high dimensional dataset. It has a wide range of applications, such as analysing high dimensional sensor data or DNA…

Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…