Search results for " dimensionality"
showing 10 items of 129 documents
Feature extraction for classification in knowledge discovery systems
2003
Dimensionality reduction is a very important step in the data mining process. In this paper, we consider feature extraction for classification tasks as a technique to overcome problems occurring because of "the curse of dimensionality". We consider three different eigenvector-based feature extraction approaches for classification. The summary of obtained results concerning the accuracy of classification schemes is presented and the issue of search for the most appropriate feature extraction method for a given data set is considered. A decision support system to aid in the integration of the feature extraction and classification processes is proposed. The goals and requirements set for the d…
More on the Dimensionality of the GHQ-12: Competitive Confirmatory Models
2019
The General Health Questionnaire (GHQ) was designed to measure minor psychiatric morbidity by assessing normal ‘healthy’ functioning and the appearance of new, distressing symptoms. Among its versions, the 12-item is one of the most used. GHQ-12’s validity and reliability have been extensively tested in samples from different populations. In the Spanish version, studies have come to different conclusions, of one, two, and three-factor structures. This research aims to present additional evidence on the factorial validity of the Spanish version of the GHQ-12, using competitive confirmatory models. Three samples of workers (N= 525, 414 and 540) were used to test a set of substantive models pr…
Forward-backward equations for nonlinear propagation in axially invariant optical systems
2004
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dir…
Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis
2016
Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance…
Transfer Learning with Convolutional Networks for Atmospheric Parameter Retrieval
2018
The Infrared Atmospheric Sounding Interferometer (IASI) on board the MetOp satellite series provides important measurements for Numerical Weather Prediction (NWP). Retrieving accurate atmospheric parameters from the raw data provided by IASI is a large challenge, but necessary in order to use the data in NWP models. Statistical models performance is compromised because of the extremely high spectral dimensionality and the high number of variables to be predicted simultaneously across the atmospheric column. All this poses a challenge for selecting and studying optimal models and processing schemes. Earlier work has shown non-linear models such as kernel methods and neural networks perform w…
Unsupervised Anomaly and Change Detection With Multivariate Gaussianization
2022
Anomaly detection (AD) is a field of intense research in remote sensing (RS) image processing. Identifying low probability events in RS images is a challenging problem given the high dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While a plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary, especially now with the data deluge problem. In this article, we propose an unsupervised method for detecting anomalies and changes …
Gaussianizing the Earth: Multidimensional Information Measures for Earth Data Analysis
2021
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is challenging because spatio-temporal data is high-dimensional, heterogeneous and has non-linear characteristics. In this paper, we apply multivariate Gaussianization for probability density estimation which is robust to dimensionality, comes with statistical guarantees, and is easy to apply. In addition, this methodology allows us to estimate information-theoretic measures to characterize multivariate densities: information, entropy, total correlation, and mutual in…
PRINCIPAL POLYNOMIAL ANALYSIS
2014
© 2014 World Scientific Publishing Company. This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves instead of straight lines. Contrarily to previous approaches PPA reduces to performing simple univariate regressions which makes it computationally feasible and robust. Moreover PPA shows a number of interesting analytical properties. First PPA is a volume preserving map which in turn guarantees the existence of the inverse. Second such an inverse can be obtained…
Dimensionality Reduction via Regression in Hyperspectral Imagery
2015
This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The pro…
Transfer of arbitrary two-qubit states via a spin chain
2015
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-1/2 network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin-excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Ref. [Phys. Rev. A 8…