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Benediktsson, “Linear versus nonlinear pca for the classification of hyperspectral data based on the extended morphological profiles,” Geoscience and Remote Sensing
 Letters, IEEE
"... Abstract—Morphological profiles have been proposed in recent literature, as aiding tools to achieve better results for classification of remotely sensed data. Morphological profiles are in general built using features containing most of the information content of the data, such as the components der ..."
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Abstract—Morphological profiles have been proposed in recent literature, as aiding tools to achieve better results for classification of remotely sensed data. Morphological profiles are in general built using features containing most of the information content of the data, such as the components derived from principal component analysis (PCA). Recently, nonlinear PCA (NLPCA), performed by autoassociative neural network, has emerged as a good unsupervised technique to fit the information content of hyperspectral data into few components. The aim of this paper is to investigate the classification accuracies obtained using extended morphological profiles built from the features of nonlinear PCA. A comparison of the two approaches has been validated on two different datasets having different spatial and spectral resolution/coverage, over the same ground truth, and also using two different classification algorithms. The results show that the NLPCA permits to obtain better classification accuracies than using linear PCA.
Imputation of missing values for compositional data using classical and robust methods
, 2009
"... ..."
Nonlinear Principal Component Analysis: Neural Network Models and Applications
"... Nonlinear principal component analysis (NLPCA) as a nonlinear generalisation of standard principal component analysis (PCA) means to generalise the principal components from straight lines to curves. This chapter aims to provide an extensive description of the autoassociative neural network approa ..."
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Nonlinear principal component analysis (NLPCA) as a nonlinear generalisation of standard principal component analysis (PCA) means to generalise the principal components from straight lines to curves. This chapter aims to provide an extensive description of the autoassociative neural network approach for NLPCA. Several network architectures will be discussed including the hierarchical, the circular, and the inverse model with special emphasis to missing data. Results are shown from applications in the field of molecular biology. This includes metabolite data analysis of a cold stress experiment in the model plant Arabidopsis thaliana and gene expression analysis of the reproductive cycle of the malaria parasite Plasmodium falciparum within infected red blood cells.
Missing value imputation with unsupervised backpropagation
 Computational Intelligence, page To Appear
, 2014
"... Many data mining and data analysis techniques operate on dense matrices or complete tables of data. Realworld data sets, however, often contain unknown values. Even many classification algorithms that are designed to operate with missing values still exhibit deteriorated accuracy. One approach to h ..."
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Many data mining and data analysis techniques operate on dense matrices or complete tables of data. Realworld data sets, however, often contain unknown values. Even many classification algorithms that are designed to operate with missing values still exhibit deteriorated accuracy. One approach to handling missing values is to fill in (impute) the missing values. In this paper, we present a technique for unsupervised learning called Unsupervised Backpropagation (UBP), which trains a multilayer perceptron to fit to the manifold sampled by a set of observed pointvectors. We evaluate UBP with the task of imputing missing values in datasets, and show that UBP is able to predict missing values with significantly lower sumsquared error than other collaborative filtering and imputation techniques. We also demonstrate with 24 datasets and 9 supervised learning algorithms that classification accuracy is usually higher when randomlywithheld values are imputed using UBP, rather than with other methods.
Analyzing periodic phenomena by circular PCA
 In Bioinformatics Research and Development. [Lecture Notes in Computer Science] Volume 4414. Edited by: Hochreiter M, Wagner R
"... Abstract. Experimental time courses often reveal a nonlinear behaviour. Analysing these nonlinearities is even more challenging when the observed phenomenon is cyclic or oscillatory. This means, in general, that the data describe a circular trajectory which is caused by periodic gene regulation. Non ..."
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Abstract. Experimental time courses often reveal a nonlinear behaviour. Analysing these nonlinearities is even more challenging when the observed phenomenon is cyclic or oscillatory. This means, in general, that the data describe a circular trajectory which is caused by periodic gene regulation. Nonlinear PCA (NLPCA) is used to approximate this trajectory by a curve referred to as nonlinear component. Which, in order to analyse cyclic phenomena, must be a closed curve hence a circular component. Here, a neural network with circular units is used to generate circular components. This circular PCA is applied to gene expression data of a time course of the intraerythrocytic developmental cycle (IDC) of the malaria parasite Plasmodium falciparum. As a result, circular PCA provides a model which describes continuously the transcriptional variation throughout the IDC. Such a computational model can then be used to comprehensively analyse the molecular behaviour over time including the identification of relevant genes at any chosen time point. Key words: gene expression, nonlinear PCA, neural networks, nonlinear dimensionality reduction, Plasmodium falciparum 1
DETECTION OF ANOMALIES PRODUCED BY BURIED ARCHAEOLOGICAL STRUCTURES USING NONLINEAR PRINCIPAL COMPONENT ANALYSIS APPLIED TO AIRBORNE HYPERSPECTRAL IMAGE
, 2013
"... In this paper, airborne hyperspectral data have been exploited by means of Nonlinear Principal Component Analysis (NLPCA) to test their effectiveness as a tool for archaeological prospection, evaluating their potential for detecting anomalies related to buried archaeological structures. In the liter ..."
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In this paper, airborne hyperspectral data have been exploited by means of Nonlinear Principal Component Analysis (NLPCA) to test their effectiveness as a tool for archaeological prospection, evaluating their potential for detecting anomalies related to buried archaeological structures. In the literature, the NLPCA was used to decorrelate the information related to a hyperspectral image. The resulting nonlinear principal components (NLPCs) contain information related to different land cover types and biophysical properties, such as vegetation coverage or soil wetness. From this point of view, NLPCA applied to airborne hyperspectral data was exploited to test their effectiveness and capability in highlighting the anomalies related to buried archaeological structures. Each component obtained from the NLPCA has been interpreted in order to assess any tonal anomalies. As a matter of a fact, since every analyzed component exhibited anomalies different in terms of size and intensity, the Separability Index (SI) was applied for measuring the tonal difference of the anomalies with respect to the surrounding area. SI has been evaluated for determining the potential of anomalies detection in each component. The airborne Multispectral Infrared and Visible Imaging Spectrometer (MIVIS) images, collected over the archaeological Park of Selinunte, were analyzed for this purpose. In this area, the presence of remains, not yet excavated, was reported by archaeologists. A previous analysis of this image, carried out to highlight the buried structures, appear to match the archaeological prospection. The results obtained by the present work demonstrate that the use of the NLPCA technique, compared to previous approaches emphasizes the ability
A Denoising View of Matrix Completion
"... In matrix completion, we are given a matrix where the values of only some of the entries are present, and we want to reconstruct the missing ones. Much work has focused on the assumption that the data matrix has low rank. We propose a more general assumption based on denoising, so that we expect tha ..."
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In matrix completion, we are given a matrix where the values of only some of the entries are present, and we want to reconstruct the missing ones. Much work has focused on the assumption that the data matrix has low rank. We propose a more general assumption based on denoising, so that we expect that the value of a missing entry can be predicted from the values of neighboring points. We propose a nonparametric version of denoising based on local, iterated averaging with meanshift, possibly constrained to preserve local lowrank manifold structure. The few user parameters required (the denoising scale, number of neighbors and local dimensionality) and the number of iterations can be estimated by crossvalidating the reconstruction error. Using our algorithms as a postprocessing step on an initial reconstruction (provided by e.g. a lowrank method), we show consistent improvements with synthetic, image and motioncapture data. Completing a matrix from a few given entries is a fundamental problem with many applications in machine learning, computer vision, network engineering, and data mining. Much interest in matrix
Validation of nonlinear PCA
 Neural Processing Letters, 2012
"... Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including crossvalidation and more generally ..."
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Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including crossvalidation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours overfitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.
Metabolic profiling of Arabidopsis thaliana epidermal cells
"... Metabolic phenotyping at cellular resolution may be considered one of the challenges in current plant physiology. A method is described which enables the cell typespecific metabolic analysis of epidermal cell types in Arabidopsis thaliana pavement, basal, and trichome cells. To achieve the required ..."
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Metabolic phenotyping at cellular resolution may be considered one of the challenges in current plant physiology. A method is described which enables the cell typespecific metabolic analysis of epidermal cell types in Arabidopsis thaliana pavement, basal, and trichome cells. To achieve the required high spatial resolution, single cell sampling using microcapillaries was combined with routine gas chromatographytime of flightmass spectrometry (GCTOFMS) based metabolite profiling. The identification and relative quantification of 117 mostly primary metabolites has been demonstrated. The majority, namely 90 compounds, were accessible without analytical background correction. Analyses were performed using cell typespecific pools of 200 microsampled individual cells. Moreover, among these identified metabolites, 38 exhibited differential pool sizes in trichomes, basal or pavement cells. The application of an independent component analysis confirmed the cell typespecific metabolic phenotypes. Significant pool size changes between individual cells were detectable within several classes of metabolites, namely amino acids, fatty acids and alcohols, alkanes, lipids, Ncompounds, organic acids and polyhydroxy acids, polyols, sugars, sugar conjugates and phenylpropanoids. It is demonstrated here that the combination of microsampling and GCMS based metabolite profiling provides a method to investigate the cellular metabolism of fully differentiated plant cell types in vivo.