An Optimal Algorithm for the Weighted Median Problem

Mining big data in brain imaging genetics is an emerging topic in brain science. It can uncover meaningful associations between genetic variations and brain structures and functions. Sparse canonical correlation analysis (SCCA) is introduced to discover bi-multivariate correlations with feature selection. However, these SCCA methods cannot be directly applied to big brain imaging genetics data due to two limitations. First, they have cubic complexity in the size of the matrix involved and are computational and memory intensive when the matrix becomes large. Second, the parameters in an SCCA method need to be fine-tuned in advance. This further dramatically increases the computational time, and gets severe in high-dimensional scenarios. In this paper, we propose two fast and efficient algorithms to speed up the structure-aware SCCA (S2CCA) implementations without modification to the original SCCA models. The fast algorithms employ a divide-and-conquer strategy and are easy to implement. The experimental results, compared with conventional algorithms, show that our algorithms reduce the time usage significantly. Specifically, the fast algorithms improve the computational efficiency by tens to hundreds of times compared to conventional algorithms. Besides, our algorithms yield similar correlation coefficients and canonical loading profiles to the conventional implementations. Our fast algorithms can be easily parallelized to further reduce the computational time. This indicates that the proposed fast scalable SCCA algorithms can be a powerful tool for big data analysis in brain imaging genetics.

In this paper, we propose a fast Alikhanov algorithm with nonuniform time steps for a two dimensional distributed‐order time–space fractional advection–dispersion equation. First, an efficient fast Alikhanov algorithm on the general nonuniform time steps for the evaluation of Caputo fractional derivative is presented to sharply reduce the computational work and storage, and are applied to the distributed‐order time fractional derivative or multi‐term time fractional derivative under the nonsmooth regularity assumptions. And a generalized discrete fractional Grönwall inequality is extended to multi‐term fractional derivative or distributed‐order fractional derivative for analyzing theoretically our algorithm. Then the stability and convergence of time semi‐discrete scheme are investigated. Furthermore, we derive the corresponding fully discrete scheme by finite element method and discuss its convergence. At last, the given numerical examples adequately confirm the correctness of theoretical analysis and compare the computing effectiveness between the fast algorithm and the direct method.

A computationally efficient approach to obtain vanishing points in images for camera orientation applications is presented in this paper. Modifications are made to the conventional J-linkage algorithm, named Fast J-linkage, so that the detection of vanishing points is achieved in a computationally efficient manner. This fast algorithm is then utilized to recover camera orientation or rotation matrices from video sequences. Both the computational efficiency and performance aspect of the Fast J-linkage algorithm are compared with the conventional J-linkage algorithm by examining the York Urban image database. In addition, the results of an actual camera rotation implementation is provided and validated by using inertial sensors data. The results obtained indicate the higher computational efficiency and accuracy aspects of the developed vanishing point detection.

Molecular volumes and surfaces of biomacromolecules via GEPOL: A fast and efficient algorithm

Feature selection entails identifying a subset of the most useful features that produces compatible results as the original entire set of features. A feature selection algorithm can be assessed in terms of both efficiency and effectiveness. While efficiency is concerned with the time required to find a subset of features, effectiveness is concerned with the quality of the subset of features. This paper proposes and experimentally evaluates a fast clustering-based feature selection algorithm, FAST, based on these criteria.  The FAST algorithm operates in two steps. Graph-theoretic clustering methods are used to partition characteristics into clusters in the initial stage. The most representative feature from each cluster that is strongly related to target classes is chosen in the second stage to construct a subset of features. Because the properties in various clusters are relatively independent, FAST's clustering-based technique is likely to produce a subset of valuable and independent features. We use the efficient Minimum-spanning tree clustering method to ensure FAST's efficiency. An empirical study is conducted to assess the efficiency and effectiveness of the FAST algorithm. FAST and several representative feature selection algorithms, such as FCBF, ReliefF, CFS, Consist, and FOCUS-SF, are compared to four types of well-known classifiers, including the probability-based Naive Bayes, the tree-based C4.5, the instance-based IB1, and the rule-based RIPPER, before and after feature selection. FAST not only provides smaller subsets of features but also improves the performances of the four types of classifiers, according to the findings, which were based on 35 publicly accessible real-world high-dimensional image, microarray, and text data.

We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

摘要: 针对合成孔径雷达(Synthetic aperture radar, SAR)图像目标检测中恒虚警率(Constant false alarm rate, CFAR)算法的广泛应用, 进行CFAR检测的快速算法分析具有重要研究价值. 首先概述了当前国内外对SAR图像CFAR检测快速算法的研究现状; 然后分别从快速预筛选和迭代计算方法两个方面对各类快速算法的实时性及性能进行了分析总结, 给出了四种基本CFAR检测器的迭代计算公式, 并提出了一种研究CFAR检测快速算法的基本框架, 现有的快速算法均可纳入该理论框架予以分析; 最后, 以经典双参数CFAR检测算法为例, 对该基本框架进行仿真实现和性能分析, 验证了其可行性与检测性能．结果表明: 新的CFAR检测快速算法基本框架充分融合了快速预筛选思想和迭代计算方法的优势, 有效提高了CFAR算法在SAR图像检测应用中的执行效率. 关键词: 合成孔径雷达图像 / 恒虚警率检测 / 快速算法 / 快速预筛选 / 迭代计算

Modern parallel SAT solvers rely heavily on effective clause sharing policies for their performance. The core problem being addressed by these policies can be succinctly stated as “the problem of identifying high-quality learnt clauses”. These clauses, when shared between the worker nodes of parallel solvers, should lead to better performance. The term “high-quality clauses” is often defined in terms of metrics that solver designers have identified over years of empirical study. Some of the more well-known metrics to identify high-quality clauses for sharing include clause length, literal block distance (LBD), and clause usage in propagation.In this paper, we propose a new metric aimed at identifying high-quality learnt clauses and a concomitant clause-sharing policy based on a combination of LBD and community structure of Boolean formulas. The concept of community structure has been proposed as a possible explanation for the extraordinary performance of SAT solvers in industrial instances. Hence, it is a natural candidate as a basis for a metric to identify high-quality clauses. To be more precise, our metric identifies clauses that have low LBD and low community number as ones that are high-quality for applications such as verification and testing. The community number of a clause C measures the number of different communities of a formula that the variables in C span. We perform extensive empirical analysis of our metric and clause-sharing policy, and show that our method significantly outperforms state-of-the-art techniques on the benchmark from the parallel track of the last four SAT competitions.

Enumeration of all maximal bicliques in bipartite graphs is a well-studied fundamental problem. However, a wide range of applications need less overlapping bicliques with specific size constraints instead of all the maximal bicliques. In this paper, we study a new biclique problem, called the top-k t-biclique coverage problem. A t-biclique is a biclique with a size constraint <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t$</tex> for one vertex set and the problem aims to find <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> t-bicliques maximising the coverage on the other vertex set. The top-k t-biclique coverage problem has novel applications such as finding top-k courses while maximising student engagement. We prove that this problem is NP-hard. A straightforward way to address the problem first needs to enumerate and store all t-bicliques and then greedily select <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> promising t-bicliques, leading an approximate guarantee on the coverage. However, it takes exponential space, which is impractical. We then apply a fast approximation scheme to solve this problem, which shaves the exponential space consumption by progressively updating top-k results during the t-biclique enumeration. Observing that the fast approximation algorithm takes too much time on updating the results due to the coverage is computed from scratch for each update, an online index is devised to address the drawback. Due the hardness of the problem, even the fast approximation algorithm cannot scale to large dataset. To devise a scalable solution, we then propose a heuristic algorithm running in polynomial time. Thanks for four carefully designed heuristic rules, the heuristic algorithm can find large coverage top-k t-bicliques extremely fast for large datasets. Apart from that, the heuristic result with large coverage can effectively prune unpromising enumerations in the fast greedy algorithm, which improves the efficiency of the fast approximation algorithm without compromising the approximation ratio. Extensive experiments are conducted on real datasets to justify the effectiveness and efficiency of the proposed algorithms.

Multi-objective optimization of material delivery for mixed model assembly lines with energy consideration

Block motion estimation using full search is computationally intensive. Previously proposed fast algorithms reduce the computation by limiting the number of searching locations. This is accomplished at the expense of less accuracy of motion estimation and gives rise to an appreciably higher mean squared error (MSE) for motion compensated images. We present a new fast and efficient search algorithm for block motion estimation that produces better quality performance and less computational time compared with a three-step search (TSS) algorithm. The proposed algorithms are based on the ideas of the dithering pattern for pixel decimation, multiple-candidate for pixel-decimation-based full search, and center-based distribution of the motion vector. From the experimental results, the proposed algorithm is superior to the TSS in both quality performance (about 0.2 dB) and computational complexity (about half).

Frequent itemsets are important information about databases, and efficiently mining frequent itemsets is a core problem in data mining area. The divide-and-conquer strategy is very applicable to the problem. Most algorithms adopting the strategy construct a very large number of conditional databases when mining frequent itemsets. Representations of conditional databases and methods of constructing them greatly influence the performance of such algorithms. In this study, we propose a node-set structure for representing a conditional database, and develop a novel node-set-based algorithm, NS, for mining frequent itemsets. During a mining process, all the node-sets derive from a prefix-tree storing the complete frequent itemset information about the mined database. Compared with previous conditional database representations, node-sets are compact and contiguous on which NS can be performed fast. Constructing conditional databases involves counting for items. In NS, the counting procedure and the construction procedure are blended, which saves the time for scanning conditional databases, and further, the major operations of constructing conditional databases are very simple comparisons. Experimental data show that NS outperforms several famous algorithms including FPgrowth* and LCM, ones of the fastest algorithms, for various databases.KeywordsData miningfrequent itemsetnode-set

In active noise control applications (ANC) recursive least-squared algorithms have become more and more common. The reason is that their convergence behavior is quite independent of the statistics of the input sound signal. Using such algorithms with digital finite impulse response filters, FIR, of an order N they show a typical convergence within N samples. There exist several algorithms for FIR-filters which are often called fast recursive least-squared (FRLS) or as fast transversal filters (FTF) in the related literature. The controller is usually built as a feedforward controller when these fast algorithms are used. The crucial integration of the secondary or error path is not done in the same way as for the well known LMS-algorithm. For the LMS usually the filtered-X-LMS is used. But this integration scheme does not work with those fast algorithms. Integration methods like the FASPIS-scheme are used instead. We describe a way to use these efficient algorithms in a adaptive feedback control structure.

This paper presents an efficient joint disparity-motion estimation algorithm and a fast motion estimation algorithm in an MPEG-4 compatible stereoscopic sequence codec for 3D broadcasting. In stereoscopic sequence coding, the critical problems to be solved are double bandwidth and computational complexity. However, the previous trials to reduce coding bits have increased computational complexity. In this paper, we try to implement fast algorithms for stereoscopic sequences while maintaining high coding efficiency. Joint disparity-motion estimation can increase coding efficiency and reduce the computational complexity of the stereoscopic codec by using the relationship between the disparity and motion fields. The disparity vectors are estimated by using the left and right motion vectors and the previous disparity vectors in each time frame. In order to obtain more accurate disparity vectors, we employ the spatial prediction process after joint estimation. From joint estimation and spatial prediction, we can obtain the accurately predicted disparity vectors and then increase the coding efficiency from those predicted vectors. Moreover, we propose a fast motion estimation algorithm which utilizes correlation between the motion vectors of the neighboring blocks. We confirmed that the PSNR of the proposed method is 1.0-2.0 dB higher than ones of conventional methods. In addition, the processing time is reduced by almost 1/10.

We present a fast and efficient algorithm for the semi-supervised colorization of line-art images (e.g. hand-made cartoons), based on two successive steps: 1. A geometric analysis of the stroke contours, and their closing by splines/segments, and 2. A colorization step based on the filling of the corresponding connected components, either with random colors or by extrapolating user-defined color scribbles. Our processing technique performs image colorization with a similar quality as previous state of the arts algorithms, while having a lower algorithmic complexity, leading to more possible user interactivity.