Search results for "Dimension"
showing 10 items of 2766 documents
Isometries between spaces of multiple Dirichlet series
2019
Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.
Computing variations of entropy and redundancy under nonlinear mappings not preserving the signal dimension: quantifying the efficiency of V1 cortex
2021
In computational neuroscience, the Efficient Coding Hypothesis argues that the neural organization comes from the optimization of information-theoretic goals [Barlow Proc.Nat.Phys.Lab.59]. A way to confirm this requires the analysis of the statistical performance of biological systems that have not been statistically optimized [Renart et al. Science10, Malo&Laparra Neur.Comp.10, Foster JOSA18, Gomez-Villa&Malo J.Neurophysiol.19]. However, when analyzing the information-theoretic performance, cortical magnification in the retina-cortex pathway poses a theoretical problem. Cortical magnification stands for the increase the signal dimensionality [Cowey&Rolls Exp. Brain Res.74]. Conventional mo…
Generalizability and Simplicity as Criteria in Feature Selection: Application to Mood Classification in Music
2011
Classification of musical audio signals according to expressed mood or emotion has evident applications to content-based music retrieval in large databases. Wrapper selection is a dimension reduction method that has been proposed for improving classification performance. However, the technique is prone to lead to overfitting of the training data, which decreases the generalizability of the obtained results. We claim that previous attempts to apply wrapper selection in the field of music information retrieval (MIR) have led to disputable conclusions about the used methods due to inadequate analysis frameworks, indicative of overfitting, and biased results. This paper presents a framework bas…
Adaptive framework for network traffic classification using dimensionality reduction and clustering
2012
Information security has become a very important topic especially during the last years. Web services are becoming more complex and dynamic. This offers new possibilities for attackers to exploit vulnerabilities by inputting malicious queries or code. However, these attack attempts are often recorded in server logs. Analyzing these logs could be a way to detect intrusions either periodically or in real time. We propose a framework that preprocesses and analyzes these log files. HTTP queries are transformed to numerical matrices using n-gram analysis. The dimensionality of these matrices is reduced using principal component analysis and diffusion map methodology. Abnormal log lines can then …
A novel heuristic memetic clustering algorithm
2013
In this paper we introduce a novel clustering algorithm based on the Memetic Algorithm meta-heuristic wherein clusters are iteratively evolved using a novel single operator employing a combination of heuristics. Several heuristics are described and employed for the three types of selections used in the operator. The algorithm was exhaustively tested on three benchmark problems and compared to a classical clustering algorithm (k-Medoids) using the same performance metrics. The results show that our clustering algorithm consistently provides better clustering solutions with less computational effort.
Gear classification and fault detection using a diffusion map framework
2015
This article proposes a system health monitoring approach that detects abnormal behavior of machines. Diffusion map is used to reduce the dimensionality of training data, which facilitates the classification of newly arriving measurements. The new measurements are handled with Nyström extension. The method is trained and tested with real gear monitoring data from several windmill parks. A machine health index is proposed, showing that data recordings can be classified as working or failing using dimensionality reduction and warning levels in the low dimensional space. The proposed approach can be used with any system that produces high-dimensional measurement data. peerReviewed
Interface Detection Using a Quenched-Noise Version of the Edwards-Wilkinson Equation
2015
We report here a multipurpose dynamic-interface-based segmentation tool, suitable for segmenting planar, cylindrical, and spherical surfaces in 3D. The method is fast enough to be used conveniently even for large images. Its implementation is straightforward and can be easily realized in many environments. Its memory consumption is low, and the set of parameters is small and easy to understand. The method is based on the Edwards-Wilkinson equation, which is traditionally used to model the equilibrium fluctuations of a propagating interface under the influence of temporally and spatially varying noise. We report here an adaptation of this equation into multidimensional image segmentation, an…
Combining PCA and multiset CCA for dimension reduction when group ICA is applied to decompose naturalistic fMRI data
2015
An extension of group independent component analysis (GICA) is introduced, where multi-set canonical correlation analysis (MCCA) is combined with principal component analysis (PCA) for three-stage dimension reduction. The method is applied on naturalistic functional MRI (fMRI) images acquired during task-free continuous music listening experiment, and the results are compared with the outcome of the conventional GICA. The extended GICA resulted slightly faster ICA convergence and, more interestingly, extracted more stimulus-related components than its conventional counterpart. Therefore, we think the extension is beneficial enhancement for GICA, especially when applied to challenging fMRI d…
BioImageXD: an open, general-purpose and high-throughput image-processing platform
2012
BioImageXD puts open-source computer science tools for three-dimensional visualization and analysis into the hands of all researchers, through a user-friendly graphical interface tuned to the needs of biologists. BioImageXD has no restrictive licenses or undisclosed algorithms and enables publication of precise, reproducible and modifiable workflows. It allows simple construction of processing pipelines and should enable biologists to perform challenging analyses of complex processes. We demonstrate its performance in a study of integrin clustering in response to selected inhibitors.
Online anomaly detection using dimensionality reduction techniques for HTTP log analysis
2015
Modern web services face an increasing number of new threats. Logs are collected from almost all web servers, and for this reason analyzing them is beneficial when trying to prevent intrusions. Intrusive behavior often differs from the normal web traffic. This paper proposes a framework to find abnormal behavior from these logs. We compare random projection, principal component analysis and diffusion map for anomaly detection. In addition, the framework has online capabilities. The first two methods have intuitive extensions while diffusion map uses the Nyström extension. This fast out-of-sample extension enables real-time analysis of web server traffic. The framework is demonstrated using …