In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of the nuclear norm over the spectral norm. The presented bound has improved dependence with respect to the approximation error (as compared to previous approaches), whereas the subspace -- on which we project the input matrices -- has dimensions proportional to the maximum of their nuclear rank and it is independent of the input dimensions. In addition, we provide an application of this result to linear low-dimensional embeddings. Namely, we show that any Euclidean point-set with bounded nuclear rank is amenable to projection onto number of dimensions that is independent of the input dimensionality, while achieving additive error guarantees.

The fundamental step in measuring the robustness of a system is the synthesis of the so called Process Map.This is generally based on the user raw data material.Process Maps are of fundamental importance towards the understanding of the nature of a system in that they indicate which variables are causally related and which are particularly important.This paper represent the system Map or business structure map to understand business criteria studying the various aspects of the company.The business structure map or knowledge map or Process map are used to increase the growth of the company by giving some useful measures according to the business criteria.This paper also deals with the different company strategy to reduce the risk factors.Process Map is helpful for building such knowledge successfully.Making decisions from such map in a highly complex situation requires more knowledge and resources.

Hierarchies are the most common structure used to understand the world better. In galaxies, for instance, multiple-star systems are organised in a hierarchical system. Then, governmental and company organisations are structured using a hierarchy, while the Internet, which is used on a daily basis, has a space of domain names arranged hierarchically. Since Artificial Intelligence (AI) planning portrays information about the world and reasons to solve some of world's problems, Hierarchical Task Network (HTN) planning has been introduced almost 40 years ago to represent and deal with hierarchies. Its requirement for rich domain knowledge to characterise the world enables HTN planning to be very useful, but also to perform well. However, the history of almost 40 years obfuscates the current understanding of HTN planning in terms of accomplishments, planning models, similarities and differences among hierarchical planners, and its current and objective image. On top of these issues, attention attracts the ability of hierarchical planning to truly cope with the requirements of applications from the real world. We propose a framework-based approach to remedy this situation. First, we provide a basis for defining different formal models of hierarchical planning, and define two models that comprise a large portion of HTN planners. Second, we provide a set of concepts that helps to interpret HTN planners from the aspect of their search space. Then, we analyse and compare the planners based on a variety of properties organised in five segments, namely domain authoring, expressiveness, competence, performance and applicability. Furthermore, we select Web service composition as a real-world and current application, and classify and compare the approaches that employ HTN planning to solve the problem of service composition. Finally, we conclude with our findings and present directions for future work.

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks suffer from serious problems, such as being oblivious to the statistical evidence supporting the discovered patterns, which results in the inability to separate actual structure from noise. In addition to this, one also observes a resolution limit on the size of communities, where smaller but well-defined clusters are not detectable when the network becomes large. This phenomenon occurs not only for the very popular approach of modularity optimization, which lacks built-in statistical validation, but also for more principled methods based on statistical inference and model selection, which do incorporate statistical validation in a formally correct way. Here we construct a nested generative model that, through a complete description of the entire network hierarchy at multiple scales, is capable of avoiding this limitation, and enables the detection of modular structure at levels far beyond those possible with current approaches. Even with this increased resolution, the method is based on the principle of parsimony, and is capable of separating signal from noise, and thus will not lead to the identification of spurious modules even on sparse networks. Furthermore, it fully generalizes other approaches in that it is not restricted to purely assortative mixing patterns, directed or undirected graphs, and ad hoc hierarchical structures such as binary trees. Despite its general character, the approach is tractable, and can be combined with advanced techniques of community detection to yield an efficient algorithm that scales well for very large networks.

Understanding the social and behavioral forces behind event participation is not only interesting from the viewpoint of social science, but also has important applications in the design of personalized event recommender systems.This paper takes advantage of data from a widely used location-based social network, Foursquare, to analyze event patterns in three metropolitan cities. We put forward several hypotheses on the motivating factors of user participation and confirm that social aspects play a major role in determining the likelihood of a user to participate in an event. While an explicit social filtering signal accounting for whether friends are attending dominates the factors, the popularity of an event proves to also be a strong attractor. Further, we capture an implicit social signal by performing random walks in a high dimensional graph that encodes the place type preferences of friends and that proves especially suited to identify relevant niche events for users. Our findings on the extent to which the various temporal, spatial and social aspects underlie users' event preferences lead us to further hypothesize that a combination of factors better models users' event interests. We verify this through a supervised learning framework. We show that for one in three users in London and one in five users in New York and Chicago it identifies the exact event the user would attend among the pool of suggestions.

Emission from a class of benzene-based molecules known as Polycyclic Aromatic Hydrocarbons (PAHs) dominates the infrared spectrum of star-forming regions. The observed emission appears to arise from the combined emission of numerous PAH species, each with its unique spectrum. Linear superposition of the PAH spectra identifies this problem as a source separation problem. It is, however, of a formidable class of source separation problems given that different PAH sources potentially number in the hundreds, even thousands, and there is only one measured spectral signal for a given astrophysical site. Fortunately, the source spectra of the PAHs are known, but the signal is also contaminated by other spectral sources. We describe our ongoing work in developing Bayesian source separation techniques relying on nested sampling in conjunction with an ON/OFF mechanism enabling simultaneous estimation of the probability that a particular PAH species is present and its contribution to the spectrum.

We present a new application and covering number bound for the framework of "Machine Learning with Operational Costs (MLOC)," which is an exploratory form of decision theory. The MLOC framework incorporates knowledge about how a predictive model will be used for a subsequent task, thus combining machine learning with the decision that is made afterwards. In this work, we use the MLOC framework to study a problem that has implications for power grid reliability and maintenance, called the Machine Learning and Traveling Repairman Problem ML&TRP. The goal of the ML&TRP is to determine a route for a "repair crew," which repairs nodes on a graph. The repair crew aims to minimize the cost of failures at the nodes, but as in many real situations, the failure probabilities are not known and must be estimated. The MLOC framework allows us to understand how this uncertainty influences the repair route. We also present new covering number generalization bounds for the MLOC framework.

Solving challenging computational problems involving time has been a critical component in the development of artificial intelligence systems almost since the inception of the field. This book provides a concise introduction to the core computational elements of temporal reasoning for use in AI systems for planning and scheduling, as well as systems that extract temporal information from data. It presents a survey of temporal frameworks based on constraints, both qualitative and quantitative, as well as of major temporal consistency techniques. The book also introduces the reader to more recent extensions to the core model that allow AI systems to explicitly represent temporal preferences and temporal uncertainty. This book is intended for students and researchers interested in constraint-based temporal reasoning.

Sparse representation based classification (SRC) has been proved to be a simple, effective and robust solution to face recognition. As it gets popular, doubts on the necessity of enforcing sparsity starts coming up, and primary experimental results showed that simply changing the $l_1$-norm based regularization to the computationally much more efficient $l_2$-norm based non-sparse version would lead to a similar or even better performance. However, that's not always the case. Given a new classification task, it's still unclear which regularization strategy (i.e., making the coefficients sparse or non-sparse) is a better choice without trying both for comparison. In this paper, we present as far as we know the first study on solving this issue, based on plenty of diverse classification experiments. We propose a scoring function for pre-selecting the regularization strategy using only the dataset size, the feature dimensionality and a discrimination score derived from a given feature representation. Moreover, we show that when dictionary learning is taking into account, non-sparse representation has a more significant superiority to sparse representation. This work is expected to enrich our understanding of sparse/non-sparse collaborative representation for classification and motivate further research activities.

This paper considers the problem of low-dimensional visualisation of very high dimensional information sources for the purpose of situation awareness in the maritime environment. In response to the requirement for human decision support aids to reduce information overload (and specifically, data amenable to inter-point relative similarity measures) appropriate to the below-water maritime domain, we are investigating a preliminary prototype topographic visualisation model. The focus of the current paper is on the mathematical problem of exploiting a relative dissimilarity representation of signals in a visual informatics mapping model, driven by real-world sonar systems. An independent source model is used to analyse the sonar beams from which a simple probabilistic input model to represent uncertainty is mapped to a latent visualisation space where data uncertainty can be accommodated. The use of euclidean and non-euclidean measures are used and the motivation for future use of non-euclidean measures is made. Concepts are illustrated using a simulated 64 beam weak SNR dataset with realistic sonar targets.