51 research outputs found
Enhancing Hyperspectral Image Quality using Nonlinear PCA
International audienceIn this paper, we propose a new method aiming at reducing the noise in hyperspectral images. It is based on the nonlinear generalization of Principal Component Analysis (NLPCA). The NLPCA is performed by an auto associative neural network that have the hyperspectral image as input and is trained to reconstruct the same image at the output. Thanks to its bottleneck structure, the AANN forces the hyper spectral image to be projected in a lower dimensionality feature space where noise as well as both linear and nonlinear correlations between spectral bands are removed. This process permits to obtain enhancements in terms of hyperspectral image quality. Experiments are conducted on different real hyper spectral images, with different contexts and resolutions. The results are qualitatively and quantitatively discussed and demonstrate the interest of the proposed method as compared to traditional approaches
Técnicas baseadas em subespaços e aplicações
Doutoramento em Engenharia ElectrónicaEste trabalho focou-se no estudo de técnicas de sub-espaço tendo em vista as
aplicações seguintes: eliminação de ruído em séries temporais e extracção de
características para problemas de classificação supervisionada. Foram estudadas
as vertentes lineares e não-lineares das referidas técnicas tendo como ponto de
partida os algoritmos SSA e KPCA. No trabalho apresentam-se propostas para
optimizar os algoritmos, bem como uma descrição dos mesmos numa abordagem
diferente daquela que é feita na literatura. Em qualquer das vertentes, linear ou
não-linear, os métodos são apresentados utilizando uma formulação algébrica
consistente. O modelo de subespaço é obtido calculando a decomposição em
valores e vectores próprios das matrizes de kernel ou de correlação/covariância
calculadas com um conjunto de dados multidimensional.
A complexidade das técnicas não lineares de subespaço é discutida,
nomeadamente, o problema da pre-imagem e a decomposição em valores e
vectores próprios de matrizes de dimensão elevada. Diferentes algoritmos de préimagem
são apresentados bem como propostas alternativas para a sua
optimização. A decomposição em vectores próprios da matriz de kernel baseada
em aproximações low-rank da matriz conduz a um algoritmo mais eficiente- o
Greedy KPCA.
Os algoritmos são aplicados a sinais artificiais de modo a estudar a influência dos
vários parâmetros na sua performance. Para além disso, a exploração destas
técnicas é extendida à eliminação de artefactos em séries temporais biomédicas
univariáveis, nomeadamente, sinais EEG.This work focuses on the study of linear and non-linear subspace projective
techniques with two intents: noise elimination and feature extraction. The
conducted study is based on the SSA, and Kernel PCA algorithms.
Several approaches to optimize the algorithms are addressed along with a
description of those algorithms in a distinct approach from the one made in the
literature. All methods presented here follow a consistent algebraic formulation
to manipulate the data. The subspace model is formed using the elements from
the eigendecomposition of kernel or correlation/covariance matrices computed
on multidimensional data sets.
The complexity of non-linear subspace techniques is exploited, namely the preimage
problem and the kernel matrix dimensionality. Different pre-image
algorithms are presented together with alternative proposals to optimize them.
In this work some approximations to the kernel matrix based on its low rank
approximation are discussed and the Greedy KPCA algorithm is introduced.
Throughout this thesis, the algorithms are applied to artificial signals in order to
study the influence of the several parameters in their performance.
Furthermore, the exploitation of these techniques is extended to artefact
removal in univariate biomedical time series, namely, EEG signals.FCT - SFRH/BD/28404/200
Two-phase incremental kernel PCA for learning massive or online datasets
As a powerful nonlinear feature extractor, kernel principal component analysis (KPCA) has been widely adopted in many machine learning applications. However, KPCA is usually performed in a batch mode, leading to some potential problems when handling massive or online datasets. To overcome this drawback of KPCA, in this paper, we propose a two-phase incremental KPCA (TP-IKPCA) algorithm which can incorporate data into KPCA in an incremental fashion. In the first phase, an incremental algorithm is developed to explicitly express the data in the kernel space. In the second phase, we extend an incremental principal component analysis (IPCA) to estimate the kernel principal components. Extensive experimental results on both synthesized and real datasets showed that the proposed TP-IKPCA produces similar principal components as conventional batch-based KPCA but is computationally faster than KPCA and its several incremental variants. Therefore, our algorithm can be applied to massive or online datasets where the batch method is not available
Two-phase incremental kernel PCA for learning massive or online datasets
As a powerful nonlinear feature extractor, kernel principal component analysis (KPCA) has been widely adopted in many machine learning applications. However, KPCA is usually performed in a batch mode, leading to some potential problems when handling massive or online datasets. To overcome this drawback of KPCA, in this paper, we propose a two-phase incremental KPCA (TP-IKPCA) algorithm which can incorporate data into KPCA in an incremental fashion. In the first phase, an incremental algorithm is developed to explicitly express the data in the kernel space. In the second phase, we extend an incremental principal component analysis (IPCA) to estimate the kernel principal components. Extensive experimental results on both synthesized and real datasets showed that the proposed TP-IKPCA produces similar principal components as conventional batch-based KPCA but is computationally faster than KPCA and its several incremental variants. Therefore, our algorithm can be applied to massive or online datasets where the batch method is not available
Visualizing Natural Image Statistics
Natural image statistics is an important area of research in cognitive sciences and computer vision. Visualization of statistical results can help identify clusters and anomalies as well as analyze deviation, distribution and correlation. Furthermore, they can provide visual abstractions and symbolism for categorized data. In this paper, we begin our study of visualization of image statistics by considering visual representations of power spectra, which are commonly used to visualize different categories of images. We show that they convey a limited amount of statistical information about image categories and their support for analytical tasks is ineffective. We then introduce several new visual representations, which convey different or more information about image statistics. We apply ANOVA to the image statistics to help select statistically more meaningful measurements in our design process. A task-based user evaluation was carried out to compare the new visual representations with the conventional power spectra plots. Based on the results of the evaluation, we made further improvement of visualizations by introducing composite visual representations of image statistics
Principal Component Analysis
This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as image processing, biometric, face recognition and speech processing. It also includes the core concepts and the state-of-the-art methods in data analysis and feature extraction
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