Kernel Methods

Resumo: A vulnerabilidade se tornou um conceito utilizado em diferentes áreas da ciência, a geografia utiliza esse conhecimento como um suporte para análise da sociedade e do ambiente físico, compreendendo dessa forma vulnerabilidade como um elemento presente no espaço geográfico. Quando analisado a vulnerabilidade a partir da sociedade, existem diversas subáreas, como vulnerabilidade em saúde, ambiental, econômica, social. Compreender a capacidade que um indivíduo, família, grupo ou uma população inteira, tem para enfrentar, suportar e se recuperar de um evento danoso, com origem natural ou social. Sendo assim a vulnerabilidade social como uma condição é o objetivo central desta pesquisa, que teve como proposta desenvolver um Índice de Vulnerabilidade Social (IVS), para população do cadastro único no perímetro urbano do Distrito Sede do município de Londrina-PR entre 2015-2017, uma população que pode apresentar características sociais de baixo poder aquisitivo, conflitos sociais, alto índice de desemprego, moradias em situações precárias ou a utilização de programas sociais, e como recorte espacial o perímetro urbano do Distrito Sede de Londrina-PR, a população do cadastro único. Para a construção do índice foi utilizada a análise de componentes principais, uma técnica estatística que permite aumentar a capacidade de interpretação de inúmeras variáveis. Como referências bibliográficas foram utilizados os autores, Katzman (1999), Busso (2001), Cutter (2003), Neto (2008), Marandola (2011) e Cunha (2013), que possibilitam unir as perspectivas da vulnerabilidade territorial, com a perspectiva da vulnerabilidade familiar e individual, permitindo a geração de IVS, baseado em informações sociodemográficas e a presença ou ausência do Estado. A teoria foi aplicada em um banco de dados onde as observações eram famílias, que eram representadas por pontos, em uma primeira espacialização, em um segundo passo foi aplicado a técnica de kernel, a qual cria áreas (células espaciais) de padrões a partir das informações pontuais, facilitando a leitura espacial dos aglomerados dos pontos. Para construção dessas células espaciais, foi estipulado um raio de 150 metros de aproximação de cada observação, ou seja, cada família, e a informação contida em cada célula é o valor da média aritmética do índice de cada ponto. Os resultados alcançados demostraram que existe uma relação entre maior intensidade da vulnerabilidade social com as regiões periféricas pobres, a ausência do Estado ou sua presença em situação precária, com as áreas que um dia foram ou são ocupações irregulares e conjuntos habitacionais populares. Entretanto algumas áreas mais centrais do perímetro urbano se caracterizaram com alta vulnerabilidade social, essas explicadas por assentamentos precários atuais, ou por uma presença de forma precária do Estado. Por último foi possível visualizar que as áreas em que a vulnerabilidade social estava manifestada, caracterizam-se por possuir uma própria extensão territorial, como um elemento do espaço geográfico, mostrando sua própria escala de análise, e demonstrando um espaço heterogêneo.
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Abstract: The vulnerability has become a concept used in different areas of science. The geography uses this knowledge as a support for the analysis of society and the physical environment, this way we understand vulnerability as a presente element in the geographic space. When analyzing vulnerability from society there are several subareas such as health, environmental, economic and social vulnerablities. Understand the capacity that an individual, family, group or an entire population has to face, endure and recover from a harmful event with natural or social origin. Thus, social vulnerability as a condition is the main objective of this research, which had as a proposal to develop a Social Vulnerability Index (IVS), for the population of the single register in the urban perimeter of the Headquarters District of Londrina-PR between 2015-2017, a population that can present social characteristics of low acquisitive power, social conflicts, high unemployment rate, habitation in straitened situations or the use of social programs and as a space cutout of the urban perimeter of the Londrina-PR Headquarters single registration. In this Index creation, it was used the analysis of the main component, a statistical technique that allows to increase the capacity of the interpretation of numerous variables. As a bibliographic source, the authors, Katzman (1999), Busso (2001), Cutter (2003), Neto (2008), Marandola (2011) and Cunha (2013) were used to link the perspectives of territorial vulnerability with the perspective of the family and individual vulnerability allowing the generation of IVS based on sociodemographic information and the presence or absence of the State. The theory was applied in a database where the observations were families which were represented by points, first was spatialization, and in a second step was applied the kernel technique which creates areas (space cells) of patterns from the information, facilitating the space reading of the clusters points. For the creation of these spacial cells, it was stipulated a radius of 150 meters of approximation of each observation, that is, each contained information in each cell is the arithmetic average of the each point?s index. The results show that there is a relation between greater intensity of social vulnerability and poor peripheral regions,the absence of the State or its presence in precarious situations with areas that once were or are irregular occupations and popular housing complex. However, central areas of the urban perimeter were characterized by high social vulnerability as explained by current precarious settlements, or by a precarious State presence. Finally, it was possible to visualize that the areas which social vulnerability was manifested are characterized by having a territorial extension as an element of geographic space, showing its own scale of analysis and demonstrating a heterogeneous space.

Detecting overlapping structures and identifying non-linearly-separable clusters with complex shapes are two major issues in clustering. This paper presents two kernel based methods that produce overlapping clusters with both linear and nonlinear boundaries. To improve separability of input patterns, we used for both methods Mercer kernel technique. First, we propose Kernel Overlapping K-means I (KOKMI), a centroid based method, generalizing kernel k-means to produce non-disjoint clusters with nonlinear separations. Second, we propose Kernel Overlapping K-means II (KOKMII), a medoid based method improving the previous method in terms of efficiency and complexity. Experiments performed on non-linearly-separable and real multi-labeled data sets show that proposed learning methods outperform the existing ones.

Information about the Earth’s surface is required in many wide-scale applications. Land cover/use
classification using remotely sensed images is one of the most common applications in remote sensing,
and many algorithms have been developed and applied for this purpose in the literature. Support vector
machines (SVMs) are a group of supervised classification algorithms that have been recently used in the
remote sensing field. The classification accuracy produced by SVMs may show variation depending on
the choice of the kernel function and its parameters. In this study, SVMs were used for land cover
classification of Gebze district of Turkey using Landsat ETM+ and Terra ASTER images. Polynomial and
radial basis kernel functions with their estimated optimum parameters were applied for the
classification of the data sets and the results were analyzed thoroughly. Results showed that SVMs,
especially with the use of radial basis function kernel, outperform the maximum likelihood classifier in
terms of overall and individual class accuracies. Some important findings were also obtained concerning
the changes in land use/cover in the study area. This study verifies the effectiveness and robustness of
SVMs in the classification of remotely sensed images.

Logistic regression is a linear binary classification algorithm frequently used for classification problems. In this paper we present its kernel version which is used for classification of non-linearly separable problems. We briefly introduce the concept of multiple kernel learning and apply it to kernel logistic regression. We elaborate the performance differences between classical, kernel logistic regression and its stochas-tic variant (both classical and kernel logistic regression).

Imaging spectroscopy, also known as hyperspectral imaging, has been transformed in less than 30 years from being a sparse research tool into a commodity product available to a broad user community. Currently, there is a need for standardized data processing techniques able to take into account the special properties of hyperspectral data. In this paper, we provide a seminal view on recent advances in techniques for hyperspectral image processing. Our main focus is on the design of techniques able to deal with the highdimensional nature of the data, and to integrate the spatial and spectral information. Performance of the discussed techniques is evaluated in different analysis scenarios. To satisfy time-critical constraints in specific applications, we also develop efficient parallel implementations of some of the discussed algorithms. Combined, these parts provide an excellent snapshot of the state-of-the-art in those areas, and offer a thoughtful perspective on future potentials and emerging challenges in the design of robust hyperspectral imaging algorithms.

A B S T R A C T Abnormal activity recognition is a challenging task in surveillance videos. In this paper, we propose an approach for abnormal activity recognition based on graph formulation of video activities and graph kernel support vector machine. The interaction of the entities in a video is formulated as a graph of geometric relations among space– time interest points. The vertices of the graph are spatio-temporal interest points and an edge represents the relation between appearance and dynamics around the interest points. Once the activity is represented using a graph, then for classification of the activities into normal or abnormal classes, we use binary support vector machine with graph kernel. These graph kernels provide robustness to slight topological deformations in comparing two graphs, which may occur due to the presence of noise in data. We demonstrate the efficacy of the proposed method on the publicly available standard datasets viz. UCSDped1, UCSDped2 and UMN. Our experiments demonstrate high rate of recognition and outperform the state-of-the-art algorithms.

This paper shows that learning to rank models can be applied to automatically learn complex patterns, such as relational semantic structures occurring in questions and their answer passages. This is achieved by providing the learning algorithm with a tree representation derived from the syntactic trees of questions and passages connected by relational tags, where the latter are again provided by the means of automatic classifiers, i.e., question and focus classifiers and Named Entity Recognizers. This way effective structural relational patterns are implicitly encoded in the representation and can be automatically utilized by powerful machine learning models such as kernel methods.

Principal Component Analysis (PCA) is a statistical technique for linear dimensionality reduction. Its Kernel version kernel-PCA is a prominent non-linear extension of the classical dimensionality reduction technique. In this paper, we present an experimental comparison between the classical PCA and the kernel-PCA. We briefly introduce and compare the performances of PCA with it kernel versions using different kernels including (rbf, laplace, sigmoid, polynomial). We also experiment the use of multi-kernels for PCA and show its comparison with classical PCA using circle, moons, classification, swiss roll and iris datasets.

We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.

Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian
matrix at the dual level. The dual formulation allows to build a model on a representative subgraph of the large scale network in the training phase and the model parameters are estimated in the validation stage. The KSC model has a powerful out-of-sample extension property which allows cluster affiliations for the unseen nodes of the big data network. In this paper we exploit the structure of the projections in the eigenspace during the validation stage
to automatically determine a set of increasing distance thresholds. We use these distance thresholds in the test phase to obtain multiple levels of hierarchy for the large scale network. The hierarchical structure in the network is
determined in a bottom-up fashion. We empirically showcase that real-world networks have multilevel hierarchical organization which cannot be detected efficiently by several state-of-the-art large scale hierarchical community detection techniques like the Louvain, OSLOM and Infomap methods. We show major advantage our proposed approach i.e. the ability to locate good quality clusters at both the coarser and finer levels of hierarchy using internal cluster quality metrics on 7 real-life networks.

On-line control using multivariate statistical methods has been widely used for largescale nonlinear industrial processes monitoring. Kernel principal component analysis (KPCA) is a nonlinear monitoring method that cannot be employed for dynamic systems. The adaptive KPCA (AKPCA) is developed for nonlinear and time varying processes based on moving window KPCA (MWKPCA) and weighted PCA (WPCA) to update online the KPCA model and its corresponding control limits. In the proposed AKPCA the model of history data is used to build new model after the new sample is obtained. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman benchmark shows its feasibility and advantageous performances. Key-words : adaptive kernel principal component analysis, multivariate statistical methods, nonlinear time-varying processes, moving window and weighted principle component analysis.