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We present a package which provides a general framework, including tools and algorithms, for text mining in R using the S4 class system. Using this package and the kernlab R package we explore the use of kernel methods for clustering (e.g., kernel k-means and spectral clustering) on a set of text documents, using string kernels. We compare these methods to a more traditional clustering technique like k-means on a bag of word representation of the text and evaluate the viability of kernel-based methods as a text clustering technique. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Examensarbete.

Thesis (M.S.); Submitted to Iowa State Univ., Ames, IA (US); 12 Dec 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2547" Elizabeth M. Lenihan. 12/12/2003. Report is also available in paper and microfiche from NTIS.

Στη διπλωματική εργασία αυτή ασχοληθήκαμε με την πρόβλεψη της εξόδου μη-γραμμικών συστημάτων με τη χρήση αναδρομικών αλγορίθμων που χρησιμοποιούν συναρτήσεις πυρήνα. Παρουσιάζεται ο δικός μας αναδρομικός αλγόριθμος πρόβλεψης και βλέπουμε πως αποδίδει σε σχέση με έναν άλλο ήδη υπάρχων και ιδιαίτερα δημοφιλή αλγόριθμο. Στο πρώτο κεφάλαιο δίνουμε μια σύντομη περιγραφή του προβλήματος που καλούμαστε να λύσουμε. Στη συνέχεια δείχνουμε πως οι συναρτήσεις πυρήνα μπορούν να χρησιμοποιηθούν για να μας βοηθήσουν να λύσουμε το πρόβλημα αυτό. Στο δεύτερο κεφάλαιο αναλύουμε περισσότερο τις συναρτήσεις πυρήνα και τις ιδιότητες που τις χαρακτηρίζουν. Παρουσιάζουμε τα βασικά θεωρήματα και βλέπουμε πώς διαμορφώνεται το πρόβλημα της πρόβλεψης με την εφαρμογή αυτών. Επιπλέον παρουσιάζουμε πως το πρόβλημα μας μετατρέπεται στο γνωστό πρόβλημα γραμμικών ελαχίστων τετραγώνων στην περίπτωση που χρησιμοποιήσουμε γραμμικό πυρήνα. Στο τρίτο κεφάλαιο παρουσιάζουμε τον αλγόριθμο μας, αναλύοντας το συλλογισμό που μας οδήγησε σε αυτόν. Δίνουμε επίσης μια περιγραφή ενός άλλου αλγορίθμου που χρησιμοποιείται ήδη για την επίλυση τέτοιων προβλημάτων. Στο τέταρτο κεφάλαιο γίνονται μια σειρά από προσομοιώσεις σε MATLAB οπού βλέπουμε πόσο καλά μπορεί να κάνει την πρόβλεψη των εξόδων μη-γραμικών συστημάτων ο αλγόριθμός μας. Επίσης αντιπαραθέτουμε και την απόδοση του ανταγωνιστικού αλγορίθμου. Στα πειράματα μας εξετάζουμε το σφάλμα πρόβλεψης των προαναφερθέντων αλγορίθμων, την ταχύτητα σύγκλισης τους καθώς και την σθεναρότητα τους. Τέλος παρουσιάζουμε τα συμπεράσματα μας εξηγώντας γιατί πιστεύουμε ότι η δικία μας προσέγγιση υπερτερεί της άλλης. / This dissertation deals with the problem of predicting the output of non-linear systems using recursive kernel methods. We will present our own prediction algorithm and see how it performs in relation to a widely used alternative algorithm. In the first chapter we provide a short description of the problem of non-linear prediction. We then describe how kernel methods could help us solve this problem. In the second chapter we further analyze kernel functions and their properties. We present the basic theorems and see how these affect and transform the problem at hand. Furthermore, we explain how this problem results in the linear least squares problem in case we use the linear kernel. In the third chapter we present our algorithm and reasoning that led to it. We also describe a different algorithm that is already used to predict such signals. In the fourth chapter we perform a series of simulations in the Matlab environment were we evaluate how well the two approaches predict the output. In this evaluation we consider the complexity, the error and robustness of the algorithms. Finally we present our conclusion and explain why our algorithm is superior to the alternative.

Economic agents often face situations, where there are multiple competing fore- casts available. Despite five decades of research on forecast combinations, most of the methods introduced so far fail to outperform the equal weights forecast combination in empirical applications. In this study, we gather a wide spectrum of forecast combination methods and reexamine these findings in two different classical economic times series forecasting applications. These include out-of- sample combining forecasts from the ECB Survey of Professional Forecasters and forecasts of the realized volatility of the U.S. Treasury futures log-returns. We asses the performance of artificial predictions markets, a class of machine learning methods, which has not yet been applied to the problem of combin- ing economic times series forecasts. Furthermore, we propose a new simple method called Market for Kernels, which is designed specifically for combining time series forecasts. We found that equal weights can be significantly out- performed by several forecast combinations, including Bates-Granger methods and artificial prediction markets in the ECB Survey of Professional Forecasters application and by almost all examined forecast combinations in the financial application. We also found that the Market for Kernels forecast...

[pt] Muitos problemas reais em modelagem computacional requerem o uso de aproximação de funções. Em alguns casos a função a ser avaliada no computador é muito complexa, portanto seria desejável que ela fosse substituída por uma função mais simples e mais eficiente de ser calculada. Para fazer isso, calcula-se o valor da função escalar f em um conjunto de N pontos {x1, x2, . . . , XN}, onde x(i) (pertence a) R(n), e faz-se uma estimativa dos valores dessa função f em qualquer outro ponto através de um método de interpolação. Um método de interpolação é qualquer procedimento que toma um conjunto de restrições e determina uma boa função que satisfaça essas condições. O método de interpolação de Shepard originalmente calcula o valor estimado dessa função num ponto qualquer x (pertence a) R(N) como uma média ponderada dos valores da função original nas N amostras dadas. Sendo que o peso para cada amostra x(i) é função das potências negativas das distâncias euclidianas entre os pontos x e x(i). Os núcleos K: R(N) × R(N) (EM) R são funções que correspondem ao produto interno no espaço de Hilbert F da imagem dos pontos x e z por uma função phi (conjunto vazio) : R(N) (EM) F, ou seja K(x, z) = < phi (conjunto vazio) (x), phi (conjunto vazio) (z) >. Na prática, as funções núcleos representam implicitamente o mapeamento feito pela função phi (conjunto vazio) , ou seja, se define qual núcleo usar e não qual phi (conjunto vazio) usar. Esse trabalho propõe uma modificação do método de interpolação de Shepard que é uma simples substituição no método original: ao invés de usar a distância euclidiana entre os pontos x e xi sugere-se usar a distância entre as imagens dos pontos x e x(I) por phi (conjunto vazio) no espaço de Hilbert F, que pode ser calculada diretamente com o uso da função núcleo K. Os resultados mostram que essa pequena modificação gera resultados melhores quando comparados com o método de Shepard original. / [en] Several real problem in computational modeling require function approximations. In some cases, the function to be evaluated in the computer is very complex, so it would be nice if this function could be substituted by a simpler and efficient one. To do so, the function f is sampled in a set of N pontos {x1, x2, . . . , xN}, where x(i) (is an element of) R(n), and then an estimate for the value of f in any other point is done by an interpolation method. An interpolation method is any procedure that takes a set of constraints and determines a nice function that satisfies such conditions. The Shepard interpolation method originally calculates the estimate of F(x) for some x (is an element of) R(n) as a weighted mean of the N sampled values of f. The weight for each sample xi is a function of the negative powers of the euclidian distances between the point x and xi. Kernels K : R(n) ×R(n) (IN) R are functions that correspond to an inner product on some Hilbert space F that contains the image of the points x and z by a function phi (the empty set) : R(n) (IN) F, i.e. k(x, z) =< phi (the empty set) (x), phi (the empty set) (z) >. In practice, the kernels represent implicitly the mapping phi (the empty set), i.e. it is more suitable to defines which kernel to use instead of which function phi (the empty set). This work proposes a simple modification on the Shepard interpolation method that is: to substitute the euclidian distance between the points x and xi by a distance between the image of these two point by phi (the empty set) in the Hilbert space F, which can be computed directly with the kernel k. Several tests show that such simple modification has better results when compared to the original method.

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Les images médicales sont utilisées afin de représenter l'anatomie. Le caractère non- linéaire d'imagerie médicale rendent leur analyse difficile. Dans cette thèse, nous nous intéressons à l'analyse d'images médicales du point de vue de la théorie statistique de l'apprentissage. Tout d'abord, nous examinons méthodes de régularisation. Dans cette direction, nous introduisons une nouvelle méthode de régularisation, la k-support regularized SVM. Cet algorithme étend la SVM régularisée `1 à une norme mixte de toutes les deux normes `1 et `2. Ensuite, nous nous intéressons un problème de comparaison des graphes. Les graphes sont une technique utilisée pour la représentation des données ayant une structure héritée. L'exploitation de ces données nécessite la capacité de comparer des graphes. Malgré le progrès dans le domaine des noyaux sur graphes, les noyaux sur graphes existants se concentrent à des graphes non-labellisés ou labellisés de façon discrète, tandis que la comparaison de graphes labellisés par des vecteurs continus, demeure un problème de recherche ouvert. Nous introduisons une nouvelle méthode, l'algorithme de Weisfeiler-Lehman pyramidal et quantifié afin d'aborder le problème de la comparaison des graphes labellisés par des vecteurs continus. Notre algorithme considère les statistiques de motifs sous arbre, basé sur l'algorithme Weisfeiler-Lehman ; il utilise une stratégie de quantification pyramidale pour déterminer un nombre logarithmique de labels discrets. Globalement, les graphes étant des objets mathématiques fondamentaux et les méthodes de régularisation étant utilisés pour contrôler des problèmes mal-posés, notre algorithmes pourraient appliqués sur un grand éventail d'applications. / Medical images have been used to depict the anatomy or function. Their high-dimensionality and their non-linearity nature makes their analysis a challenging problem. In this thesis, we address the medical image analysis from the viewpoint of statistical learning theory. First, we examine regularization methods for analyzing MRI data. In this direction, we introduce a novel regularization method, the k-support regularized Support Vector Machine. This algorithm extends the 1 regularized SVM to a mixed norm of both `1 and `2 norms. We evaluate our algorithm in a neuromuscular disease classification task. Second, we approach the problem of graph representation and comparison for analyzing medical images. Graphs are a technique to represent data with inherited structure. Despite the significant progress in graph kernels, existing graph kernels focus on either unlabeled or discretely labeled graphs, while efficient and expressive representation and comparison of graphs with continuous high-dimensional vector labels, remains an open research problem. We introduce a novel method, the pyramid quantized Weisfeiler-Lehman graph representation to tackle the graph comparison problem for continuous vector labeled graphs. Our algorithm considers statistics of subtree patterns based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings. We evaluate our algorithm on two different tasks with real datasets. Overall, as graphs are fundamental mathematical objects and regularization methods are used to control ill-pose problems, both proposed algorithms are potentially applicable to a wide range of domains.

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