Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version

Trainable COSFIRE filters for vessel delineation with application to retinal images

Retinal imaging provides a non-invasive opportunity for the diagnosis of several medical pathologies. The automatic segmentation of the vessel tree is an important pre-processing step which facilitates subsequent automatic processes that contribute to such diagnosis. We introduce a novel method for the automatic segmentation of vessel trees in retinal fundus images. We propose a filter that selectively responds to vessels and that we call B-COSFIRE with B standing for bar which is an abstraction for a vessel. It is based on the existing COSFIRE (Combination Of Shifted Filter Responses) approach. A B-COSFIRE filter achieves orientation selectivity by computing the weighted geometric mean of the output of a pool of Difference-of-Gaussians filters, whose supports are aligned in a collinear manner. It achieves rotation invariance efficiently by simple shifting operations. The proposed filter is versatile as its selectivity is determined from any given vessel-like prototype pattern in an automatic configuration process. We configure two B-COSFIRE filters, namely symmetric and asymmetric, that are selective for bars and bar-endings, respectively. We achieve vessel segmentation by summing up the responses of the two rotation-invariant B-COSFIRE filters followed by thresholding. The results that we achieve on three publicly available data sets (DRIVE: Se = 0.7655, Sp = 0.9704; STARE: Se = 0.7716, Sp = 0.9701; CHASE_DB1: Se = 0.7585, Sp = 0.9587) are higher than many of the state-of-the-art methods. The proposed segmentation approach is also very efficient with a time complexity that is significantly lower than existing methods.peer-reviewe

Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences

We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approximates the ideal predictor from data. We discuss the reliability of CSSR, its data requirements, and its performance in simulations. Finally, we compare our approach to existing methods using variable-length Markov models and cross-validated hidden Markov models, and show theoretically and experimentally that our method delivers results superior to the former and at least comparable to the latter.Comment: 8 pages, 4 figure

A Distributed, Architecture-Centric Approach to Computing Accurate Recommendations from Very Large and Sparse Datasets

The use of recommender systems is an emerging trend today, when user behavior information is abundant. There are many large datasets available for analysis because many businesses are interested in future user opinions. Sophisticated algorithms that predict such opinions can simplify decision-making, improve customer satisfaction, and increase sales. However, modern datasets contain millions of records, which represent only a small fraction of all possible data. Furthermore, much of the information in such sparse datasets may be considered irrelevant for making individual recommendations. As a result, there is a demand for a way to make personalized suggestions from large amounts of noisy data. Current recommender systems are usually all-in-one applications that provide one type of recommendation. Their inflexible architectures prevent detailed examination of recommendation accuracy and its causes. We introduce a novel architecture model that supports scalable, distributed suggestions from multiple independent nodes. Our model consists of two components, the input matrix generation algorithm and multiple platform-independent combination algorithms. A dedicated input generation component provides the necessary data for combination algorithms, reduces their size, and eliminates redundant data processing. Likewise, simple combination algorithms can produce recommendations from the same input, so we can more easily distinguish between the benefits of a particular combination algorithm and the quality of the data it receives. Such flexible architecture is more conducive for a comprehensive examination of our system. We believe that a user's future opinion may be inferred from a small amount of data, provided that this data is most relevant. We propose a novel algorithm that generates a more optimal recommender input. Unlike existing approaches, our method sorts the relevant data twice. Doing this is slower, but the quality of the resulting input is considerably better. Furthermore, the modular nature of our approach may improve its performance, especially in the cloud computing context. We implement and validate our proposed model via mathematical modeling, by appealing to statistical theories, and through extensive experiments, data analysis, and empirical studies. Our empirical study examines the effectiveness of accuracy improvement techniques for collaborative filtering recommender systems. We evaluate our proposed architecture model on the Netflix dataset, a popular (over 130,000 solutions), large (over 100,000,000 records), and extremely sparse (1.1\%) collection of movie ratings. The results show that combination algorithm tuning has little effect on recommendation accuracy. However, all algorithms produce better results when supplied with a more relevant input. Our input generation algorithm is the reason for a considerable accuracy improvement

Rank Conditioned Rank Selection Filters for Signal Restoration

A class of nonlinear filters called rank conditioned rank selection (RCRS) filters is developed and analyzed in this paper. The RCRS filters are developed within the general framework of rank selection(RS) filters, which are filters constrained to output an order statistic from the observation set. Many previously proposed rank order based filters can be formulated as RS filters. The only difference between such filters is in the information used in deciding which order statistic to output. The information used by RCRS filters is the ranks of selected input samples, hence the name rank conditioned rank selection filters. The number of input sample ranks used is referred to as the order of the RCRS filter. The order can range from zero to the number of samples in the observation window, giving the filters valuable flexibility. Low-order filters can give good performance and are relatively simple to optimize and implement. If improved performance is demanded, the order can be increased but at the expense of filter simplicity. In this paper, many statistical and deterministic properties of the RCRS filters are presented. A procedure for optimizing over the class of RCRS filters is also presented. Finally, extensive computer simulation results that illustrate the performance of RCRS filters in comparison with other techniques in image restoration applications are presented