Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting where each point has a few arbitrarily corrupted components. Yet, in applications of SVD or PCA such as robust collaborative filtering or bioinformatics, malicious agents, defective genes, or simply corrupted or contaminated experiments may effectively yield entire points that are completely corrupted. We present an efficient convex optimization-based algorithm we call Outlier Pursuit, that under some mild assumptions on the uncorrupted points (satisfied, e.g., by the standard generative assumption in PCA problems) recovers the exact optimal low-dimensional subspace, and identifies the corrupted points. Such identification of corrupted points that do not conform to the low-dimensional approximation, is of paramount interest in bioinformatics and financial applications, and beyond. Our techniques involve matrix decomposition using nuclear norm minimization, however, our results, setup, and approach, necessarily differ considerably from the existing line of work in matrix completion and matrix decomposition, since we develop an approach to recover the correct column space of the uncorrupted matrix, rather than the exact matrix itself. In any problem where one seeks to recover a structure rather than the exact initial matrices, techniques developed thus far relying on certificates of optimality, will fail. We present an important extension of these methods, that allows the treatment of such problems.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

In this paper we introduce a method for extending binary qualitative direction calculi with adjustable granularity like OPRAm or the star calculus with a granular distance concept. This method is similar to the concept of extending points with an internal reference direction to get oriented points which are the basic entities in the OPRAm calculus. Even if the spatial objects are from a geometrical point of view infinitesimal small points locally available reference measures are attached. In the case of OPRAm, a reference direction is attached. The same principle works also with local reference distances which are called elevations. The principle of attaching references features to a point is called hidden feature attachment.

In video games, virtual characters' decision systems often use a simplified representation of the world. To increase both their autonomy and believability we want those characters to be able to learn this representation from human players. We propose to use a model called growing neural gas to learn by imitation the topology of the environment. The implementation of the model, the modifications and the parameters we used are detailed. Then, the quality of the learned representations and their evolution during the learning are studied using different measures. Improvements for the growing neural gas to give more information to the character's model are given in the conclusion.

In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are different sets of data. This is contrasted to the conventional measure for probabilities as well as to the proposed measure of possibilities. We define what characteristics this measure of plausibility should have. In getting to the conception of this measure, we explore the relation of plausibility to abductive reasoning, and to Bayesian probabilities. We also compare with the Dempster-Schaefer theory of evidence, which also has its own definition for plausibility. Abduction can be associated with biconditionality in inference rules, and this provides a platform to relate to the Collins-Michalski theory of plausibility. Finally, using a formalism for wiring logic onto Hopfield neural networks, we ask if this is relevant in obtaining this measure.

Software cost estimation is one of the prerequisite managerial activities carried out at the software development initiation stages and also repeated throughout the whole software life-cycle so that amendments to the total cost are made. In software cost estimation typically, a selection of project attributes is employed to produce effort estimations of the expected human resources to deliver a software product. However, choosing the appropriate project cost drivers in each case requires a lot of experience and knowledge on behalf of the project manager which can only be obtained through years of software engineering practice. A number of studies indicate that popular methods applied in the literature for software cost estimation, such as linear regression, are not robust enough and do not yield accurate predictions. Recently the dual variables Ridge Regression (RR) technique has been used for effort estimation yielding promising results. In this work we show that results may be further improved if an AI method is used to automatically select appropriate project cost drivers (inputs) for the technique. We propose a hybrid approach combining RR with a Genetic Algorithm, the latter evolving the subset of attributes for approximating effort more accurately. The proposed hybrid cost model has been applied on a widely known high-dimensional dataset of software project samples and the results obtained show that accuracy may be increased if redundant attributes are eliminated.

Case Based Reasoning and particularly Estimation by Analogy, has been used in a number of problem-solving areas, such as cost estimation. Conventional methods, despite the lack of a sound criterion for choosing nearest projects, were based on estimation using a fixed and predetermined number of neighbors from the entire set of historical instances. This approach puts boundaries to the estimation ability of such algorithms, for they do not take into consideration that every project under estimation is unique and requires different handling. The notion of distributions of distances together with a distance metric for distributions help us to adapt the proposed method (we call it DD-EbA) each time to a specific case that is to be estimated without loosing in prediction power or computational cost. The results of this paper show that the proposed technique achieves the above idea in a very efficient way.

A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences for which there is general agreement on how to continue. However, there are less regular sequences for which this assessment is less certain. There are sequences for which every continuation is perceived to be arbitrary. I would like to present a mathematical model that reflects these opinions and perceptions with the aid of a valuation function. It is necessary to apply a rich set of invariant features of position sequences to ensure the quality of this model. All other properties of the model are arbitrary.

Mining association rules is a task of data mining, which extracts knowledge in the form of significant implication relation of useful items (objects) from a database. Mining multilevel association rules uses concept hierarchies, also called taxonomies and defined as relations of type 'is-a' between objects, to extract rules that items belong to different levels of abstraction. These rules are more useful, more refined and more interpretable by the user. Several algorithms have been proposed in the literature to discover the multilevel association rules. In this article, we are interested in the problem of discovering multi-level frequent itemsets under constraints, involving the user in the research process. We proposed a technique for modeling and interpretation of constraints in a context of use of concept hierarchies. Three approaches for discovering multi-level frequent itemsets under constraints were proposed and discussed: Basic approach, "Test and Generate" approach and Pruning based Approach.

Recent years have witnessed the popularity of using rank minimization as a regularizer for various signal processing and machine learning problems. As rank minimization problems are often converted to nuclear norm minimization (NNM) problems, they have to be solved iteratively and each iteration requires computing a singular value decomposition (SVD). Therefore, their solution suffers from the high computation cost of multiple SVDs. To relieve this issue, we propose using the block Lanczos method to compute the partial SVDs, where the principal singular subspaces obtained in the previous iteration are used to start the block Lanczos procedure. To avoid the expensive reorthogonalization in the Lanczos procedure, the block Lanczos procedure is performed for only a few steps. Our block Lanczos with warm start (BLWS) technique can be adopted by different algorithms that solve NNM problems. We present numerical results on applying BLWS to Robust PCA and Matrix Completion problems. Experimental results show that our BLWS technique usually accelerates its host algorithm by at least two to three times.