Search results for "curse of dimensionality"
showing 10 items of 100 documents
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
Dynamic integration of classifiers in the space of principal components
2003
Recent research has shown the integration of multiple classifiers to be one of the most important directions in machine learning and data mining. It was shown that, for an ensemble to be successful, it should consist of accurate and diverse base classifiers. However, it is also important that the integration procedure in the ensemble should properly utilize the ensemble diversity. In this paper, we present an algorithm for the dynamic integration of classifiers in the space of extracted features (FEDIC). It is based on the technique of dynamic integration, in which local accuracy estimates are calculated for each base classifier of an ensemble, in the neighborhood of a new instance to be pr…
The situational version of the Brief Cope: Dimensionality and relationships with goal-related variables
2015
This study is aimed at investigating the dimensionality of the situational version of the Brief COPE, a questionnaire that is frequently used to assess a broad range of coping responses to specific difficulties, by comparing five different factor models highlighted in previous studies. It also aimed at exploring the relationships among coping responses, personal goal commitment and progress. The study involved 606 adults (male = 289) ranging in age from 19 to 71. Using confirmatory factor analysis, we compared five models and assessed relationships of coping responses with goal commitment and progress. The results confirmed the theoretical factor structure of the situational Brief COPE. All…
Extraction of Endmembers from Spectral Mixtures
1999
Abstract Linear spectral mixture modeling (LSMM) divides each ground resolution element into its constituent materials using endmembers which represent the spectral characteristics of the cover types. However, it is difficult to identify and estimate the spectral signature of pure components or endmembers which form the scene, since they vary with the scale and purpose of the study. We propose three different methods to estimate the spectra of pure components from a set of unknown mixture spectra. Two of the methods consist in different optimization procedures based on objective functions defined from the coordinate axes of the dominant factors. The third one consists in the design of a neu…
Synthetic phenomenology and high-dimensional buffer hypothesis
2012
Synthetic phenomenology typically focuses on the analysis of simplified perceptual signals with small or reduced dimensionality. Instead, synthetic phenomenology should be analyzed in terms of perceptual signals with huge dimensionality. Effective phenomenal processes actually exploit the entire richness of the dynamic perceptual signals coming from the retina. The hypothesis of a high-dimensional buffer at the basis of the perception loop that generates the robot synthetic phenomenology is analyzed in terms of a cognitive architecture for robot vision the authors have developed over the years. Despite the obvious computational problems when dealing with high-dimensional vectors, spaces wit…
Nonlinear Distribution Regression for Remote Sensing Applications
2020
In many remote sensing applications, one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms, such as neural networks, random forests, or the Gaussian processes, are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e., collectively associated with a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning (MIL) or distribution regression (DR). This article introduces a nonlinear (kern…
Random Feature Approximation for Online Nonlinear Graph Topology Identification
2021
Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments con…
Multivariate GARCH estimation via a Bregman-proximal trust-region method
2011
The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low…
Model selection in linear mixed-effect models
2019
Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or ra…
Building up adjusted indicators of students' evaluation of university courses using generalized item response models
2012
This article advances a proposal for building up adjusted composite indicators of the quality of university courses from students’ assessments. The flexible framework of Generalized Item Response Models is adopted here for controlling the sources of heterogeneity in the data structure that make evaluations across courses not directly comparable. Specifically, it allows us to: jointly model students’ ratings to the set of items which define the quality of university courses; explicitly consider the dimensionality of the items composing the evaluation form; evaluate and remove the effect of potential confounding factors which may affect students’ evaluation; model the intra-cluster variabilit…