Fuzzy, integer and fractional-order control: Application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Approximate entropy normalized measures for analyzing social neurobiological systems

When considering time series data of variables describing agent interactions in social neurobiological systems, measures of regularity can provide a global understanding of such system behaviors. Approximate entropy (ApEn) was introduced as a nonlinear measure to assess the complexity of a system behavior by quantifying the regularity of the generated time series. However, ApEn is not reliable when assessing and comparing the regularity of data series with short or inconsistent lengths, which often occur in studies of social neurobiological systems, particularly in dyadic human movement systems. Here, the authors present two normalized, nonmodified measures of regularity derived from the original ApEn, which are less dependent on time series length. The validity of the suggested measures was tested in well-established series (random and sine) prior to their empirical application, describing the dyadic behavior of athletes in team games. The authors consider one of the ApEn normalized measures to generate the 95th percentile envelopes that can be used to test whether a particular social neurobiological system is highly complex (i.e., generates highly unpredictable time series). Results demonstrated that suggested measures may be considered as valid instruments for measuring and comparing complexity in systems that produce time series with inconsistent lengths.

Global localization with non-quantized local image features

In the field of appearance-based robot localization, the mainstream approach uses a quantized representation of local image features. An alternative strategy is the exploitation of raw feature descriptors, thus avoiding approximations due to quantization. In this work, the quantized and non-quantized representations are compared with respect to their discriminativity, in the context of the robot global localization problem. Having demonstrated the advantages of the non-quantized representation, the paper proposes mechanisms to reduce the computational burden this approach would carry, when applied in its simplest form. This reduction is achieved through a hierarchical strategy which gradually discards candidate locations and by exploring two simplifying assumptions about the training data. The potential of the non-quantized representation is exploited by resorting to the entropy-discriminativity relation. The idea behind this approach is that the non-quantized representation facilitates the assessment of the distinctiveness of features, through the entropy measure. Building on this finding, the robustness of the localization system is enhanced by modulating the importance of features according to the entropy measure. Experimental results support the effectiveness of this approach, as well as the validity of the proposed computation reduction methods.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Estudo de falha em placas laminadas usando métodos analíticos e numéricos

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Manutenção

Stress in university students and cardiovascular response to academic stressors

Introduction: University students are frequently exposed to events that can cause stress and anxiety, producing elevated cardiovascular responses. Repeated exposure to academic stress has implications to students’ success and well-being and may contribute to the development of long-term health problems. Objective: To identify stress levels and coping strategies in university students and assess the impact of stress experience in heart rate variability (HRV). Methods: 17 university students, 19-23 years, completed the University Students Stress Inventory, the Depression Anxiety Stress Scales and the Ways of Coping Questionnaire. Two 24h-Holter recordings were performed, on academic activity days, including one of them an exam situation. Results: Students tend to present moderate stress levels, and prefer problem-focused coping strategies in order to manage stress. Exam situations are perceived as significant stressors. Although we found no significant differences in HRV (SDNN), between days with and without an exam, we registered a lower SDNN score and a variation in heart rate (HR) related to exam situation (maximum HR peak at 10 minutes before the exam, and total HR recovery 20 minutes after the exam), reflecting sympathetic activation due to stress. Conclusions: These results suggest that academic events, especially those related to exam situations, are the cause of stress in university students, with implications at cardiovascular level, underlying the importance of interventions that help these students improve their coping skills and optimize stress management, in order to improve academic achievement and promote well-being and quality of life.

18F-FDG measurement in primary lung cancer: SUV normalization to different distribution volumes

Introduction: Standard Uptake Value (SUV) is a measurement of the uptake in a tumour normalized on the basis of a distribution volume and is used to quantify 18F-Fluorodeoxiglucose (FDG) uptake in tumors, such as primary lung tumor. Several sources of error can affect its accuracy. Normalization can be based on body weight, body surface area (BSA) and lean body mass (LBM). The aim of this study is to compare the influence of 3 normalization volumes in the calculation of SUV: body weight (SUVW), BSA (SUVBSA) and LBM (SUVLBM), with and without glucose correction, in patients with known primary lung tumor. The correlation between SUV and weight, height, blood glucose level, injected activity and time between injection and image acquisition is evaluated. Methods: Sample included 30 subjects (8 female and 22 male) with primary lung tumor, with clinical indication for 18F-FDG Positron Emission Tomography (PET). Images were acquired on a Siemens Biography according to the department’s protocol. Maximum pixel SUVW was obtained for abnormal uptake focus through semiautomatic VOI with Quantification 3D isocontour (threshold 2.5). The concentration of radioactivity (kBq/ml) was obtained from SUVW, SUVBSA, SUVLBM and the glucose corrected SUV were mathematically obtained. Results: Statistically significant differences between SUVW, SUVBSA and SUVLBM and between SUVWgluc, SUVBSAgluc and SUVLBMgluc were observed (p=0.000<0.05). The blood glucose level showed significant positive correlations with SUVW (r=0.371; p=0.043) and SUVLBM (r=0.389; p=0.034). SUVBSA showed independence of variations with the blood glucose level. Conclusion: The measurement of a radiopharmaceutical tumor uptake normalized on the basis of different distribution volumes is still variable. Further investigation on this subject is recommended.

Otimização de placas compósitas laminadas utilizando redes neuronais e enxames de partículas

Trabalho Final de mestrado para obtenção do grau de Mestre em engenharia Mecância

O projeto de literacia da informação numa biblioteca da saúde: o caso da Biblioteca da ESTeSL

Introdução – Ao aumento exponencial de informação, sobretudo a científica, não corresponde obrigatoriamente a melhoria de qualidade na pesquisa e no uso da mesma. O conceito de literacia da informação ganha pertinência e destaque, na medida em que abarca competências que permitem reconhecer quando é necessária a informação e de atuar de forma eficiente e efetiva na sua obtenção e utilização. A biblioteca académica assume, neste contexto, o papel de parceiro privilegiado, preparando o momento em que o estudante se sente capaz de produzir e registar novo conhecimento através da escrita. Objectivo – A Biblioteca da ESTeSL reestruturou as sessões desenvolvidas desde o ano lectivo 2002/2003 e deu início a um projecto mais formal denominado «Saber usar a informação de forma eficiente e eficaz». Objectivos: a) promover a melhoria da qualidade dos trabalhos académicos e científicos; b) contribuir para a diminuição do risco de plágio; c) aumentar a confiança dos estudantes nas suas capacidades de utilização dos recursos de informação; d) incentivar uma participação mais ativa em sala de aulas; e) colaborar para a integração dos conteúdos pedagógicos e das várias fontes de informação. Método – Dinamizaram-se várias sessões de formação de curta duração, versando diferentes temas associados à literacia de informação, designadamente: 1) Pesquisa de informação com sessões dedicadas à MEDLINE, RCAAP, SciELO, B-ON e Scopus; 2) Factor de impacto das revistas científicas: Journal Citation Reports e SciMAGO; 3) Como fazer um resumo científico?; 4) Como estruturar o trabalho científico?; 5) Como fazer uma apresentação oral?; 6) Como evitar o plágio?; 7) Referenciação bibliográfica usando a norma de Vancouver; 8) Utilização de gestores de referências bibliográficas: ZOTERO (primeira abordagem para os estudantes de 1º ano de licenciatura) e a gestão de referências e rede académica de informação com o MENDELEY (direcionado para estudantes finalistas, mestrandos, docentes e investigadores). O projecto foi apresentado à comunidade académica no site da ESTeSL; cada sessão foi divulgada individualmente no site e por email. Em 2015, a divulgação investiu na nova página da Biblioteca (https://estesl.biblio.ipl.pt/), que alojava informações e recursos abordados nas formações. As inscrições eram feitas por email, sem custos associados ou limite mínimo ou máximo de sessões para participar. Resultados – Em 2014 registaram-se 87 inscrições. Constatou-se a presença de, pelo menos, um participante em cada sessão de formação. Em 2015, o total de inscrições foi de 190. Foram reagendadas novas sessões a pedido dos estudantes cujos horários não eram compatíveis com os inicialmente agendados. Foram então organizados dois dias de formação seguida (cerca de 4h em cada dia) com conteúdos selecionados pelos estudantes. Registou-se, nestas sessões, a presença contante de cerca de 30 estudantes em sala. No total, as sessões da literacia da informação contaram com estudantes de licenciatura de todos os anos, estudantes de mestrado, docentes e investigadores (internos e externos à ESTeSL). Conclusões – Constata-se a necessidade de introdução de novos conteúdos no projeto de literacia da informação. O tempo, os conteúdos e o interesse demonstrado por aqueles que dele usufruíram evidenciam que este é um projeto que está a ganhar o seu espaço na comunidade da ESTeSL e que a literacia da informação contribui de forma efetiva para a construção e para a produção de conhecimento no meio académico.

Viscosity measurements of compressed liquid dipropyl and dibutyl adipates

The paper reports viscosity measurements of compressed liquid dipropyl (DPA) and dibutyl (DBA) adipates obtained with two vibrating wire sensors developed in our group. The vibrating wire instruments were operated in the forced oscillation, or steady-state mode. The viscosity measurements of DPA were carried out in a range of pressures up to 18. MPa and temperatures from (303 to 333). K, and DBA up to 65. MPa and temperature from (303 to 373). K, covering a total range of viscosities from (1.3 to 8.3). mPa. s. The required density data of the liquid samples were obtained in our laboratory using an Anton Paar vibrating tube densimeter and were reported in a previous paper. The viscosity results were correlated with density, using a modified hard-spheres scheme. The root mean square deviation of the data from the correlation is less than (0.21 and 0.32)% and the maximum absolute relative deviations are within (0.43 and 0.81)%, for DPA and DBA respectively. No data for the viscosity of both adipates could be found in the literature. Independent viscosity measurements were also performed, at atmospheric pressure, using an Ubbelohde capillary in order to compare with the vibrating wire results. The expanded uncertainty of these results is estimated as ±1.5% at a 95% confidence level. The two data sets agree within the uncertainty of both methods. © 2015 Published by Elsevier B.V.

Novel coordination polymers with (Pyrazolato)-based tectons: catalytic activity in the peroxidative oxidation of alcohols and cyclohexane

Coupling five rigid or flexible bis(pyrazolato)based tectons with late transition metal ions allowed us to isolate 18 coordination polymers (CPs). As assessed by thermal analysis, all of them possess a remarkable thermal stability, their decomposition temperatures lying in the range of 340-500 degrees C. As demonstrated by N-2 adsorption measurements at 77 K, their Langmuir specific surface areas span the rather vast range of 135-1758 m(2)/g, in agreement with the porous or dense polymeric architectures retrieved by powder X-ray diffraction structure solution methods. Two representative families of CPs, built up with either rigid or flexible spacers, were tested as catalysts in (0 the microwave-assisted solvent-free peroxidative oxidation of alcohols by t-BuOOH, and (ii) the peroxidative oxidation of cydohexane to cydohexanol and cydohexanone by H2O2 in acetonitrile. Those CPs bearing the rigid spacer, concurrently possessing higher specific surface areas, are more active than the corresponding ones with the flexible spacer. Moreover, the two copper(I)-containing CPs investigated exhibit the highest efficiency in both reactions, leading selectively to a maximum product yield of 92% (and TON up to 1.5 x 10(3)) in the oxidation of 1-phenylethanol and of 11% in the oxidation of cydohexane, the latter value being higher than that granted by the current industrial process.

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Text classification using compression-based dissimilarity measures

Arguably, the most difficult task in text classification is to choose an appropriate set of features that allows machine learning algorithms to provide accurate classification. Most state-of-the-art techniques for this task involve careful feature engineering and a pre-processing stage, which may be too expensive in the emerging context of massive collections of electronic texts. In this paper, we propose efficient methods for text classification based on information-theoretic dissimilarity measures, which are used to define dissimilarity-based representations. These methods dispense with any feature design or engineering, by mapping texts into a feature space using universal dissimilarity measures; in this space, classical classifiers (e.g. nearest neighbor or support vector machines) can then be used. The reported experimental evaluation of the proposed methods, on sentiment polarity analysis and authorship attribution problems, reveals that it approximates, sometimes even outperforms previous state-of-the-art techniques, despite being much simpler, in the sense that they do not require any text pre-processing or feature engineering.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.