In this work, we propose a general method for recovering low-rank three-order tensors, in which the data can be deformed by some unknown transformation and corrupted by arbitrary sparse errors. Since the unfolding matrices of a tensor are interdependent, we introduce auxiliary variables and relax the hard equality constraints by the augmented Lagrange multiplier method. To improve the computational efficiency, we introduce a proximal gradient step to the alternating direction minimization method. We have provided proof for the convergence of the linearized version of the problem which is the inner loop of the overall algorithm. Both simulations and experiments show that our methods are more efficient and effective than previous work. The proposed method can be easily applied to simultaneously rectify and align multiple images or videos frames. In this context, the state-of-the-art algorithms RASL'' and "TILT'' can be viewed as two special cases of our work, and yet each only performs part of the function of our method."

The Markov chain is a convenient tool to represent the dynamics of complex systems such as traffic and social systems, where probabilistic transition takes place between internal states. A Markov chain is characterized by initial-state probabilities and a state-transition probability matrix. In the traditional setting, a major goal is to figure out properties of a Markov chain when those probabilities are known. This paper tackles an inverse version of the problem: we find those probabilities from partial observations at a limited number of states. The observations include the frequency of visiting a state and the rate of reaching a state from another. Practical examples of this task include traffic monitoring systems in cities, where we need to infer the traffic volume on every single link on a road network from a very limited number of observation points. We formulate this task as a regularized optimization problem for probability functions, which is efficiently solved using the notion of natural gradient. Using synthetic and real-world data sets including city traffic monitoring data, we demonstrate the effectiveness of our method.

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

In a context of document co-clustering, we define a new similarity measure which iteratively computes similarity while combining fuzzy sets in a three-partite graph. The fuzzy triadic similarity (FT-Sim) model can deal with uncertainty offers by the fuzzy sets. Moreover, with the development of the Web and the high availability of storage spaces, more and more documents become accessible. Documents can be provided from multiple sites and make similarity computation an expensive processing. This problem motivated us to use parallel computing. In this paper, we introduce parallel architectures which are able to treat large and multi-source data sets by a sequential, a merging or a splitting-based process. Then, we proceed to a local and a central (or global) computing using the basic FT-Sim measure. The idea behind these architectures is to reduce both time and space complexities thanks to parallel computation.

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

This article presents a probabilistic sub-tree alignment model and its application to tree-to-tree machine translation. Unlike previous work, we do not resort to surface heuristics or expensive annotated data, but instead derive an unsupervised model to infer the syntactic correspondence between two languages. More importantly, the developed model is syntactically-motivated and does not rely on word alignments. As a by-product, our model outputs a sub-tree alignment matrix encoding a large number of diverse alignments between syntactic structures, from which machine translation systems can efficiently extract translation rules that are often filtered out due to the errors in 1-best alignment. Experimental results show that the proposed approach outperforms three state-of-the-art baseline approaches in both alignment accuracy and grammar quality. When applied to machine translation, our approach yields a +1.0 BLEU improvement and a -0.9 TER reduction on the NIST machine translation evaluation corpora. With tree binarization and fuzzy decoding, it even outperforms a state-of-the-art hierarchical phrase-based system.

We present NaturalOWL, a natural language generation system that produces texts describing individuals or classes of OWL ontologies. Unlike simpler OWL verbalizers, which typically express a single axiom at a time in controlled, often not entirely fluent natural language primarily for the benefit of domain experts, we aim to generate fluent and coherent multi-sentence texts for end-users. With a system like NaturalOWL, one can publish information in OWL on the Web, along with automatically produced corresponding texts in multiple languages, making the information accessible not only to computer programs and domain experts, but also end-users. We discuss the processing stages of NaturalOWL, the optional domain-dependent linguistic resources that the system can use at each stage, and why they are useful. We also present trials showing that when the domain-dependent llinguistic resources are available, NaturalOWL produces significantly better texts compared to a simpler verbalizer, and that the resources can be created with relatively light effort.

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.

Defeasible inheritance networks are a non-monotonic framework that deals with hierarchical knowledge. On the other hand, rational closure is acknowledged as a landmark of the preferential approach to non-monotonic reasoning. We will combine these two approaches and define a new non-monotonic closure operation for propositional knowledge bases that combines the advantages of both. Then we redefine such a procedure for Description Logics (DLs), a family of logics well-suited to model structured information. In both cases we will provide a simple reasoning method that is built on top of the classical entailment relation and, thus, is amenable of an implementation based on existing reasoners. Eventually, we evaluate our approach on well-known landmark test examples.

Many natural language processing (NLP) applications require the computation of similarities between pairs of syntactic or semantic trees. Many researchers have used tree edit distance for this task, but this technique suffers from the drawback that it deals with single node operations only. We have extended the standard tree edit distance algorithm to deal with subtree transformation operations as well as single nodes. The extended algorithm with subtree operations, TED+ST, is more effective and flexible than the standard algorithm, especially for applications that pay attention to relations among nodes (e.g. in linguistic trees, deleting a modifier subtree should be cheaper than the sum of deleting its components individually). We describe the use of TED+ST for checking entailment between two Arabic text snippets. The preliminary results of using TED+ST were encouraging when compared with two string-based approaches and with the standard algorithm.