Search results for "Nonlinear dimensionality reduction"

2016

AbstractThe different factors involved in the growth process of complex networks imprint valuable information in their observable topologies. How to exploit this information to accurately predict structural network changes is the subject of active research. A recent model of network growth sustains that the emergence of properties common to most complex systems is the result of certain trade-offs between node birth-time and similarity. This model has a geometric interpretation in hyperbolic space, where distances between nodes abstract this optimisation process. Current methods for network hyperbolic embedding search for node coordinates that maximise the likelihood that the network was pro…

Making nonlinear manifold learning models interpretable: The manifold grand tour

2015

Smooth nonlinear topographic maps of the data distribution to guide a Grand Tour visualisation.Prioritisation of data linear views that are most consistent with data structure in the maps.Useful visualisations that cannot be obtained by other more classical approaches. Dimensionality reduction is required to produce visualisations of high dimensional data. In this framework, one of the most straightforward approaches to visualising high dimensional data is based on reducing complexity and applying linear projections while tumbling the projection axes in a defined sequence which generates a Grand Tour of the data. We propose using smooth nonlinear topographic maps of the data distribution to…

Dimensionality reduction via regression on hyperspectral infrared sounding data

2014

This paper introduces a new method for dimensionality reduction via regression (DRR). The method generalizes Principal Component Analysis (PCA) in such a way that reduces the variance of the PCA scores. In order to do so, DRR relies on a deflationary process in which a non-linear regression reduces the redundancy between the PC scores. Unlike other nonlinear dimensionality reduction methods, DRR is easy to apply, it has out-of-sample extension, it is invertible, and the learned transformation is volume-preserving. These properties make the method useful for a wide range of applications, especially in very high dimensional data in general, and for hyperspectral image processing in particular…

Texture Classification with Generalized Fourier Descriptors in Dimensionality Reduction Context: An Overview Exploration

2008

In the context of texture classification, this article explores the capacity and the performance of some combinations of feature extraction, linear and nonlinear dimensionality reduction techniques and several kinds of classification methods. The performances are evaluated and compared in term of classification error. In order to test our texture classification protocol, the experiment carried out images from two different sources, the well known Brodatz database and our leaf texture images database.

Manifold Learning with High Dimensional Model Representations

2020

Manifold learning methods are very efficient methods for hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high input dimensional space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to p…

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…

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…

Multi-temporal and Multi-source Remote Sensing Image Classification by Nonlinear Relative Normalization

2016

Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for one image to be used successfully in other scenes. In order to adapt and transfer models across image acquisitions, one must be able to cope with datasets that are not co-registered, acquired under different illumination and atmospheric conditions, by different sensors, and with scarce ground references. Traditionally, methods based on histogram matching have been used. However, they fail when densities have very different shapes or when there is no corres…

Visible-NIR reflectance spectroscopy and manifold learning methods applied to the detection of fungal infections on citrus fruit

2015

Abstract The development of systems for automatically detecting decay in citrus fruit during quality control is still a challenge for the citrus industry. The feasibility of reflectance spectroscopy in the visible and near infrared (NIR) regions was evaluated for the automatic detection of the early symptoms of decay caused by Penicillium digitatum fungus in citrus fruit. Reflectance spectra of sound and decaying surface parts of mandarins cv. ‘Clemenvilla’ were acquired in two different spectral regions, from 650 nm to 1050 nm (visible–NIR) and from 1000 nm to 1700 nm (NIR), pointing to significant differences in spectra between sound and decaying skin for both spectral ranges. Three diffe…