Related papers: Dimensional Analysis: A Centenary Update

The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…

Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…

In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here,…

With the development of web technology, multi-modal or multi-view data has surged as a major stream for big data, where each modal/view encodes individual property of data objects. Often, different modalities are complementary to each…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…

Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…

We argue that dimensionality is not absolute, but that it depends on the scale of resolution, from the Planck to the macro scale.

Certain operator-valued functions and new generating structures (instead of generating functionals) are proposed for the analysis of equations for n-point information (n-pi). Some remarks are made concerning the intertwining of linearity…

A common method of making a theory more understandable, is by comparing it to another theory which has been better developed. Radical interpretation is a theory which attempts to explain how communication has meaning. Radical interpretation…

This paper presents exploratory techniques for multivariate data, many of them well known to French statisticians and ecologists, but few well understood in North American culture. We present the general framework of duality diagrams which…

Visual analytics using dimensionality reduction (DR) can easily be unreliable for various reasons, e.g., inherent distortions in representing the original data. The literature has thus proposed a wide range of methodologies to make DR-based…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

Multidimensional in data warehouse is a compulsion and become the most important for information delivery, without multidimensional data warehouse is incomplete. Multidimensional give the able to analyze business measurement in many…

This article advocates factorized and hybrid dimensional decompositions (FDD/HDD), as alternatives to analysis-of-variance dimensional decomposition (ADD), for second-moment statistical analysis of multivariate functions. New formulae…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…

In this paper we present several novel efficient techniques and multidimensional data structures which can improve the decision making process in many domains. We consider online range aggregation, range selection and range weighted median…

Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas…

Recurrence quantification analysis is a widely used method for characterizing patterns in time series. This article presents a comprehensive survey for conducting a wide range of recurrence-based analyses to quantify the dynamical structure…

We investigate the value of extending the completeness of a decision model along different dimensions of refinement. Specifically, we analyze the expected value of quantitative, conceptual, and structural refinement of decision models. We…