In group decision making (GDM) problems fuzzy preference relations (FPR) are widely used for representing decision makers' opinions on the set of alternatives. In order to avoid misleading solutions, the study of consistency and consensus has become a very important aspect. This article presents a simulated annealing (SA) based soft computing approach to optimize the consistency/consensus level (CCL) of a complete fuzzy preference relation in order to solve a GDM problem. Consistency level indicates as expert's preference quality and consensus level measures the degree of agreement among experts' opinions. This study also suggests the set of experts for the necessary modifications in their prescribed preference structures without intervention of any moderator.

Operating vehicles in adversarial environments between a recurring origin-destination pair requires new planning techniques. A two players zero-sum game is introduced. The goal of the first player is to minimize the expected casualties undergone by a convoy. The goal of the second player is to maximize this damage. The outcome of the game is obtained via a linear program that solves the corresponding minmax optimization problem over this outcome. Different environment models are defined in order to compute routing strategies over unstructured environments. To compare these methods for increasingly accurate representations of the environment, a grid-based model is chosen to represent the environment and the existence of a sufficient network size is highlighted. A global framework for the generation of realistic routing strategies between any two points is described. This framework requires a good assessment of the potential casualties at any location, therefore the most important parameters are identified. Finally the framework is tested on real world environments.

In domains such as biomedicine, ontologies are prominently utilized for annotating data. Consequently, aligning ontologies facilitates integrating data. Several algorithms exist for automatically aligning ontologies with diverse levels of performance. As alignment applications evolve and exhibit online run time constraints, performing the alignment in a reasonable amount of time without compromising the quality of the alignment is a crucial challenge. A large class of alignment algorithms is iterative and often consumes more time than others in delivering solutions of high quality. We present a novel and general approach for speeding up the multivariable optimization process utilized by these algorithms. Specifically, we use the technique of block-coordinate descent (BCD), which exploits the subdimensions of the alignment problem identified using a partitioning scheme. We integrate this approach into multiple well-known alignment algorithms and show that the enhanced algorithms generate similar or improved alignments in significantly less time on a comprehensive testbed of ontology pairs. Because BCD does not overly constrain how we partition or order the parts, we vary the partitioning and ordering schemes in order to empirically determine the best schemes for each of the selected algorithms. As biomedicine represents a key application domain for ontologies, we introduce a comprehensive biomedical ontology testbed for the community in order to evaluate alignment algorithms. Because biomedical ontologies tend to be large, default iterative techniques find it difficult to produce a good quality alignment within a reasonable amount of time. We align a significant number of ontology pairs from this testbed using BCD-enhanced algorithms. Our contributions represent an important step toward making a significant class of alignment techniques computationally feasible.

Tree ensembles such as random forests and boosted trees are accurate but difficult to understand, debug and deploy. In this work, we provide the inTrees (interpretable trees) framework that extracts, measures, prunes and selects rules from a tree ensemble, and calculates frequent variable interactions. An rule-based learner, referred to as the simplified tree ensemble learner (STEL), can also be formed and used for future prediction. The inTrees framework can applied to both classification and regression problems, and is applicable to many types of tree ensembles, e.g., random forests, regularized random forests, and boosted trees. We implemented the inTrees algorithms in the "inTrees" R package.

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal estimators due to the relaxation effect. To optimally estimate sparse principal subspaces, we propose a two-stage computational framework named "tighten after relax": Within the 'relax' stage, we approximately solve a convex relaxation of sparse PCA with early stopping to obtain a desired initial estimator; For the 'tighten' stage, we propose a novel algorithm called sparse orthogonal iteration pursuit (SOAP), which iteratively refines the initial estimator by directly solving the underlying nonconvex problem. A key concept of this two-stage framework is the basin of attraction. It represents a local region within which the `tighten' stage has desired computational and statistical guarantees. We prove that, the initial estimator obtained from the 'relax' stage falls into such a region, and hence SOAP geometrically converges to a principal subspace estimator which is minimax-optimal within a certain model class. Unlike most existing sparse PCA estimators, our approach applies to the non-spiked covariance models, and adapts to non-Gaussianity as well as dependent data settings. Moreover, through analyzing the computational complexity of the two stages, we illustrate an interesting phenomenon that larger sample size can reduce the total iteration complexity. Our framework motivates a general paradigm for solving many complex statistical problems which involve nonconvex optimization with provable guarantees.

Cluster analysis is a field of data analysis that extracts underlying patterns in data. One application of cluster analysis is in text-mining, the analysis of large collections of text to find similarities between documents. We used a collection of about 30,000 tweets extracted from Twitter just before the World Cup started. A common problem with real world text data is the presence of linguistic noise. In our case it would be extraneous tweets that are unrelated to dominant themes. To combat this problem, we created an algorithm that combined the DBSCAN algorithm and a consensus matrix. This way we are left with the tweets that are related to those dominant themes. We then used cluster analysis to find those topics that the tweets describe. We clustered the tweets using k-means, a commonly used clustering algorithm, and Non-Negative Matrix Factorization (NMF) and compared the results. The two algorithms gave similar results, but NMF proved to be faster and provided more easily interpreted results. We explored our results using two visualization tools, Gephi and Wordle.

Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with probability proportional to its statistical leverage score. Unfortunately, leverage scores are difficult to compute. A simple alternative is to sample rows uniformly at random. While this often works, uniform sampling will eliminate critical row information for many natural instances. We take a fresh look at uniform sampling by examining what information it does preserve. Specifically, we show that uniform sampling yields a matrix that, in some sense, well approximates a large fraction of the original. While this weak form of approximation is not enough for solving linear regression directly, it is enough to compute a better approximation. This observation leads to simple iterative row sampling algorithms for matrix approximation that run in input-sparsity time and preserve row structure and sparsity at all intermediate steps. In addition to an improved understanding of uniform sampling, our main proof introduces a structural result of independent interest: we show that every matrix can be made to have low coherence by reweighting a small subset of its rows.

We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. It shows competitive performance on standard benchmark datasets against a number of other representative algorithms in the literature. We also discuss extensions of RoBiRank to large scale problems where explicit feature vectors and scores are not given. We show that RoBiRank can be efficiently parallelized across a large number of machines; for a task that requires 386, 133 49, 824, 519 pairwise interactions between items to be ranked, RoBi-Rank finds solutions that are of dramatically higher quality than that can be found by a state-of-the-art competitor algorithm, given the same amount of wall-clock time for computation.

When a transition probability matrix is represented as the product of two stochastic matrices, one can swap the factors of the multiplication to obtain another transition matrix that retains some fundamental characteristics of the original. Since the derived matrix can be much smaller than its precursor, this property can be exploited to create a compact version of a Markov decision process (MDP), and hence to reduce the computational cost of dynamic programming. Building on this idea, this paper presents an approximate policy iteration algorithm called policy iteration based on stochastic factorization, or PISF for short. In terms of computational complexity, PISF replaces standard policy iteration's cubic dependence on the size of the MDP with a function that grows only linearly with the number of states in the model. The proposed algorithm also enjoys nice theoretical properties: it always terminates after a finite number of iterations and returns a decision policy whose performance only depends on the quality of the stochastic factorization. In particular, if the approximation error in the factorization is sufficiently small, PISF computes the optimal value function of the MDP. The paper also discusses practical ways of factoring an MDP and illustrates the usefulness of the proposed algorithm with an application involving a large-scale decision problem of real economical interest.

We describe a state-of-the-art sentiment analysis system that detects (a) the sentiment of short informal textual messages such as tweets and SMS (message-level task) and (b) the sentiment of a word or a phrase within a message (term-level task). The system is based on a supervised statistical text classification approach leveraging a variety of surface-form, semantic, and sentiment features. The sentiment features are primarily derived from novel high-coverage tweet-specific sentiment lexicons. These lexicons are automatically generated from tweets with sentiment-word hashtags and from tweets with emoticons. To adequately capture the sentiment of words in negated contexts, a separate sentiment lexicon is generated for negated words. The system ranked first in the SemEval-2013 shared task `Sentiment Analysis in Twitter' (Task 2), obtaining an F-score of 69.02 in the message-level task and 88.93 in the term-level task. Post-competition improvements boost the performance to an F-score of 70.45 (message-level task) and 89.50 (term-level task). The system also obtains state-of-the-art performance on two additional datasets: the SemEval-2013 SMS test set and a corpus of movie review excerpts. The ablation experiments demonstrate that the use of the automatically generated lexicons results in performance gains of up to 6.5 absolute percentage points.