In recent years, the advance of information and communication technologies has allowed the storage and transfer of massive amounts of data. The availability of this overwhelming amount of data stimulates a growing need to develop fast and accurate algorithms to discover useful information hidden in the data. This need is even more acute for unsupervised data, which lacks information about the categories of different instances. This dissertation addresses a crucial problem in unsupervised data analysis, which is the selection of representative instances and/or features from the data. This problem can be generally defined as the selection of the most representative columns of a data matrix, which is formally known as the Column Subset Selection (CSS) problem. Algorithms for column subset selection can be directly used for data analysis or as a pre-processing step to enhance other data mining algorithms, such as clustering. The contributions of this dissertation can be summarized as outlined below. First, a fast and accurate algorithm is proposed to greedily select a subset of columns of a data matrix such that the reconstruction error of the matrix based on the subset of selected columns is minimized. The algorithm is based on a novel recursive formula for calculating the reconstruction error, which allows the development of time and memory-efficient algorithms for greedy column subset selection. Experiments on real data sets demonstrate the effectiveness and efficiency of the proposed algorithms in comparison to the state-of-the-art methods for column subset selection. Second, a kernel-based algorithm is presented for column subset selection. The algorithm greedily selects representative columns using information about their pairwise similarities. The algorithm can also calculate a Nyström approximation for a large kernel matrix based on the subset of selected columns. In comparison to different Nyström methods, the greedy Nyström method has been empirically shown to achieve significant improvements in approximating kernel matrices, with minimum overhead in run time. Third, two algorithms are proposed for fast approximate k-means and spectral clustering. These algorithms employ the greedy column subset selection method to embed all data points in the subspace of a few representative points, where the clustering is performed. The approximate algorithms run much faster than their exact counterparts while achieving comparable clustering performance. Fourth, a fast and accurate greedy algorithm for unsupervised feature selection is proposed. The algorithm is an application of the greedy column subset selection method presented in this dissertation. Similarly, the features are greedily selected such that the reconstruction error of the data matrix is minimized. Experiments on benchmark data sets show that the greedy algorithm outperforms state-of-the-art methods for unsupervised feature selection in the clustering task. Finally, the dissertation studies the connection between the column subset selection problem and other related problems in statistical data analysis, and it presents a unified framework which allows the use of the greedy algorithms presented in this dissertation to solve different related problems.

In recent years, the advance of information and communication technologies has allowed the storage and transfer of massive amounts of data. The availability of this overwhelming amount of data stimulates a growing need to develop fast and accurate algorithms to discover useful information hidden in the data. This need is even more acute for unsupervised data, which lacks information about the categories of different instances. This dissertation addresses a crucial problem in unsupervised data analysis, which is the selection of representative instances and/or features from the data. This problem can be generally defined as the selection of the most representative columns of a data matrix, which is formally known as the Column Subset Selection (CSS) problem. Algorithms for column subset selection can be directly used for data analysis or as a pre-processing step to enhance other data mining algorithms, such as clustering. The contributions of this dissertation can be summarized as outlined below. First, a fast and accurate algorithm is proposed to greedily select a subset of columns of a data matrix such that the reconstruction error of the matrix based on the subset of selected columns is minimized. The algorithm is based on a novel recursive formula for calculating the reconstruction error, which allows the development of time and memory-efficient algorithms for greedy column subset selection. Experiments on real data sets demonstrate the effectiveness and efficiency of the proposed algorithms in comparison to the state-of-the-art methods for column subset selection. Second, a kernel-based algorithm is presented for column subset selection. The algorithm greedily selects representative columns using information about their pairwise similarities. The algorithm can also calculate a Nyström approximation for a large kernel matrix based on the subset of selected columns. In comparison to different Nyström methods, the greedy Nyström method has been empirically shown to achieve significant improvements in approximating kernel matrices, with minimum overhead in run time. Third, two algorithms are proposed for fast approximate k-means and spectral clustering. These algorithms employ the greedy column subset selection method to embed all data points in the subspace of a few representative points, where the clustering is performed. The approximate algorithms run much faster than their exact counterparts while achieving comparable clustering performance. Fourth, a fast and accurate greedy algorithm for unsupervised feature selection is proposed. The algorithm is an application of the greedy column subset selection method presented in this dissertation. Similarly, the features are greedily selected such that the reconstruction error of the data matrix is minimized. Experiments on benchmark data sets show that the greedy algorithm outperforms state-of-the-art methods for unsupervised feature selection in the clustering task. Finally, the dissertation studies the connection between the column subset selection problem and other related problems in statistical data analysis, and it presents a unified framework which allows the use of the greedy algorithms presented in this dissertation to solve different related problems.

Dans cette thèse, on aborde le problème de structuration des programmes télévisés de manière non supervisée à partir du point de vue de l'inférence grammaticale, focalisant sur la découverte de la structure des programmes récurrents à partir une collection homogène. On vise à découvrir les éléments structuraux qui sont pertinents à la structure du programme, et à l’inférence grammaticale de la structure des programmes. Des expérimentations montrent que l'inférence grammaticale permet de utiliser minimum des connaissances de domaine a priori pour atteindre la découverte de la structure des programmes. / TV program structuring raises as a major theme in last decade for the task of high quality indexing. In this thesis, we address the problem of unsupervised TV program structuring from the point of view of grammatical inference, i.e., discovering a common structural model shared by a collection of episodes of a recurrent program. Using grammatical inference makes it possible to rely on only minimal domain knowledge. In particular, we assume no prior knowledge on the structural elements that might be present in a recurrent program and very limited knowledge on the program type, e.g., to name structural elements, apart from the recurrence. With this assumption, we propose an unsupervised framework operating in two stages. The first stage aims at determining the structural elements that are relevant to the structure of a program. We address this issue making use of the property of element repetitiveness in recurrent programs, leveraging temporal density analysis to filter out irrelevant events and determine valid elements. Having discovered structural elements, the second stage is to infer a grammar of the program. We explore two inference techniques based either on multiple sequence alignment or on uniform resampling. A model of the structure is derived from the grammars and used to predict the structure of new episodes. Evaluations are performed on a selection of four different types of recurrent programs. Focusing on structural element determination, we analyze the effect on the number of determined structural elements, fixing the threshold applied on the density function as well as the size of collection of episodes. For structural grammar inference, we discuss the quality of the grammars obtained and show that they accurately reflect the structure of the program. We also demonstrate that the models obtained by grammatical inference can accurately predict the structure of unseen episodes, conducting a quantitative and comparative evaluation of the two methods by segmenting the new episodes into their structural components. Finally, considering the limitations of our work, we discuss a number of open issues in structure discovery and propose three new research directions to address in future work.