Related papers: Faster estimation of the correlation fractal dimen…
This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to explain the fractal dimension of urban form. The…
This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an…
The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…
Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents ($d_q$) can exhibit perfect scaling suggesting non zero $d_q$'s. Properties of these…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
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…
This work joins aspects of reservoir optimization, information-theoretic optimal encoding, and at its center fractal analysis. We build on the observation that, due to the recursive nature of recurrent neural networks, input sequences…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and…
Correlation filters take advantage of specific properties in the Fourier domain allowing them to be estimated efficiently: O(NDlogD) in the frequency domain, versus O(D^3 + ND^2) spatially where D is signal length, and N is the number of…
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…
This paper analyzes the performance of the Fractal Decomposition Algorithm (FDA) metaheuristic applied to low-dimensional continuous optimization problems. This algorithm was originally developed specifically to deal efficiently with…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…