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.

Phytoplankton analysis of portuguese reservoirs: a cluster analysis with R

In this work, cluster analysis is applied to a real dataset of biological features of several Portuguese reservoirs. All the statistical analysis is done using R statistical software. Several metrics and methods were explored, as well as the combination of Euclidean metric and the hierarchical Ward method. Although it did not present the best combination in terms of internal and stability validation, it was still a good solution and presented good results in terms of interpretation of the problem at hand.

Artificial Intelligence in geospatial analysis: applications of self-organizing maps in the context of geographic information science.

A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Information Systems.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Longitudinal analysis of tumor marker CEA of breast cancer patients from Braga's hospital

Allied to an epidemiological study of population of the Senology Unit of Braga’s Hospital that have been diagnosed with malignant breast cancer, we describe the progression in time of repeated measurements of tumor marker Carcinoembryonic antigen (CEA). Our main purpose is to describe the progression of this tumor marker as a function of possible risk factors and, hence, to understand how these risk factors influences that progression. The response variable, values of CEA, was analyzed making use of longitudinal models, testing for different correlation structures. The same covariates used in a previous survival analysis were considered in the longitudinal model. The reference time used was time from diagnose until death from breast cancer. For diagnostic of the models fitted we have used empirical and theoretical variograms. To evaluate the fixed term of the longitudinal model we have tested for a changing point on the effect of time on the tumor marker progression. A longitudinal model was also fitted only to the subset of patients that died from breast cancer, using the reference time as time from date of death until blood test.

Exploraty Multivariate Statistical Methods Applied to Pharmaceutical Industry CRM Data

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Spatial analysis and investigation of fire events occurrences in the Valencian Community, Spain

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Hydrologic modeling and uncertainty analysis of an ungauged watershed using mapwindow-swat

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies

Automatic Small Bowel Tumor Diagnosis by Using Multi-Scale Wavelet-Based Analysis in Wireless Capsule Endoscopy Images

BACKGROUND: Wireless capsule endoscopy has been introduced as an innovative, non-invasive diagnostic technique for evaluation of the gastrointestinal tract, reaching places where conventional endoscopy is unable to. However, the output of this technique is an 8 hours video, whose analysis by the expert physician is very time consuming. Thus, a computer assisted diagnosis tool to help the physicians to evaluate CE exams faster and more accurately is an important technical challenge and an excellent economical opportunity. METHOD: The set of features proposed in this paper to code textural information is based on statistical modeling of second order textural measures extracted from co-occurrence matrices. To cope with both joint and marginal non-Gaussianity of second order textural measures, higher order moments are used. These statistical moments are taken from the two-dimensional color-scale feature space, where two different scales are considered. Second and higher order moments of textural measures are computed from the co-occurrence matrices computed from images synthesized by the inverse wavelet transform of the wavelet transform containing only the selected scales for the three color channels. The dimensionality of the data is reduced by using Principal Component Analysis. RESULTS: The proposed textural features are then used as the input of a classifier based on artificial neural networks. Classification performances of 93.1% specificity and 93.9% sensitivity are achieved on real data. These promising results open the path towards a deeper study regarding the applicability of this algorithm in computer aided diagnosis systems to assist physicians in their clinical practice.

Learning networks and moodle use in online courses: a social network analysis study

Dissertação para obtenção do Grau de Doutor em Ciências da Educação Especialidade em Tecnologias, Redes e Multimédia na Educação e Formação

Time series morphological analysis applied to biomedical signals events detection

Dissertation submitted in the fufillment of the requirements for the Degree of Master in Biomedical Engineering

Spatial analysis of crime evolution in Portugal between 1995 and 2013

The main objective of this survey was to perform descriptive analysis of crime evolution in Portugal between 1995 and 2013. The main focus of this survey was to analyse spatial crime evolution patterns in Portuguese NUTS III regions. Most important crime types have been included into analysis. The main idea was to uncover relation between local patterns and global crime evolution; to define regions which have contributed to global crime evolution of some specific crime types and to define how they have contributed. There were many statistical reports and scientific papers which have analysed some particular crime types, but one global spatial-temporal analysis has not been found. Principal Component Analysis and multidimensional descriptive data analysis technique STATIS have been the base of the analysis. The results of this survey has shown that strong spatial and temporal crime patterns exist. It was possible to describe global crime evolution patterns and to define crime evolution patterns in NUTS III regions. It was possible to define three to four groups of crimes where each group shows similar spatial crime dynamics.

Land cover mapping analysis and urban growth modeling using remote sensing techniques

The rapid growth of big cities has been noticed since 1950s when the majority of world population turned to live in urban areas rather than villages, seeking better job opportunities and higher quality of services and lifestyle circumstances. This demographic transition from rural to urban is expected to have a continuous increase. Governments, especially in less developed countries, are going to face more challenges in different sectors, raising the essence of understanding the spatial pattern of the growth for an effective urban planning. The study aimed to detect, analyse and model the urban growth in Greater Cairo Region (GCR) as one of the fast growing mega cities in the world using remote sensing data. Knowing the current and estimated urbanization situation in GCR will help decision makers in Egypt to adjust their plans and develop new ones. These plans should focus on resources reallocation to overcome the problems arising in the future and to achieve a sustainable development of urban areas, especially after the high percentage of illegal settlements which took place in the last decades. The study focused on a period of 30 years; from 1984 to 2014, and the major transitions to urban were modelled to predict the future scenarios in 2025. Three satellite images of different time stamps (1984, 2003 and 2014) were classified using Support Vector Machines (SVM) classifier, then the land cover changes were detected by applying a high level mapping technique. Later the results were analyzed for higher accurate estimations of the urban growth in the future in 2025 using Land Change Modeler (LCM) embedded in IDRISI software. Moreover, the spatial and temporal urban growth patterns were analyzed using statistical metrics developed in FRAGSTATS software. The study resulted in an overall classification accuracy of 96%, 97.3% and 96.3% for 1984, 2003 and 2014’s map, respectively. Between 1984 and 2003, 19 179 hectares of vegetation and 21 417 hectares of desert changed to urban, while from 2003 to 2014, the transitions to urban from both land cover classes were found to be 16 486 and 31 045 hectares, respectively. The model results indicated that 14% of the vegetation and 4% of the desert in 2014 will turn into urban in 2025, representing 16 512 and 24 687 hectares, respectively.

Brazilian equity risk premium analysis: A macroeconomic approach

Double Degree Masters in Economics Program from Insper and NOVA School of Business and Economics