Related papers: Dimensional Analysis: A Centenary Update
In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
The relevance and importance of contextualizing data analytics is described. Qualitative characteristics might form the context of quantitative analysis. Topics that are at issue include: contrast, baselining, secondary data sources,…
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…
Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views…
Over the past two decades, the field of high-dimensional statistics has experienced substantial progress, driven largely by technological advances that have dramatically reduced the cost and effort for data collection and storage across a…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
Visualization of high-dimensional data is counter-intuitive using conventional graphs. Parallel coordinates are proposed as an alternative to explore multivariate data more effectively. However, it is difficult to extract relevant…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
Though the mediums for visualization are limited, the potential dimensions of a dataset are not. In many areas of scientific study, understanding the correlations between those dimensions and their uncertainties is pivotal to mining useful…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Machine learning algorithms using deep architectures have been able to implement increasingly powerful and successful models. However, they also become increasingly more complex, more difficult to comprehend and easier to fool. So far, most…
It is effective to improve the reliability and availability of large-scale cluster systems through the analysis of failures. Existed failure analysis methods understand and analyze failures from one or few dimension. The analysis results…