Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples

Reverse spatial visual top-k query

With the wide application of mobile Internet techniques an location-based services (LBS), massive multimedia data with geo-tags has been generated and collected. In this paper, we investigate a novel type of spatial query problem, named reverse spatial visual top- $k$ query (RSVQ k ) that aims to retrieve a set of geo-images that have the query as one of the most relevant geo-images in both geographical proximity and visual similarity. Existing approaches for reverse top- $k$ queries are not suitable to address this problem because they cannot effectively process unstructured data, such as image. To this end, firstly we propose the definition of RSVQ k problem and introduce the similarity measurement. A novel hybrid index, named VR 2 -Tree is designed, which is a combination of visual representation of geo-image and R-Tree. Besides, an extension of VR 2 -Tree, called CVR 2 -Tree is introduced and then we discuss the calculation of lower/upper bound, and then propose the optimization technique via CVR 2 -Tree for further pruning. In addition, a search algorithm named RSVQ k algorithm is developed to support the efficient RSVQ k query. Comprehensive experiments are conducted on four geo-image datasets, and the results illustrate that our approach can address the RSVQ k problem effectively and efficiently

Random walk with restart over dynamic graphs

Random Walk with Restart (RWR) is an appealing measure of proximity between nodes based on graph structures. Since real graphs are often large and subject to minor changes, it is prohibitively expensive to recompute proximities from scratch. Previous methods use LU decomposition and degree reordering heuristics, entailing O(|V|3) time and O(|V|2) memory to compute all (|V|2) pairs of node proximities in a static graph. In this paper, a dynamic scheme to assess RWR proximities is proposed: (1) For unit update, we characterize the changes to all-pairs proximities as the outer product of two vectors. We notice that the multiplication of an RWR matrix and its transition matrix, unlike traditional matrix multiplications, is commutative. This can greatly reduce the computation of all-pairs proximities from O(|V|3) to O(|Δ|) time for each update without loss of accuracy, where |Δ| (<<|V|2) is the number of affected proximities. (2) To avoid O(|V|2) memory for all pairs of outputs, we also devise efficient partitioning techniques for our dynamic model, which can compute all pairs of proximities segment-wisely within O(l|V|) is a user-controlled trade-off between  memory an I/O costs. (3) For bulk update, we also devise aggregation and hashing methods, which can discard many unneccessary updates further and handle chuncks of unit updates simultaneously. Our experimental results on various datasets demonstrate that our methods can be 1-2 orders of magnitude faster than other competitors while securing scalability and exactness..

Fast Exact CoSimRank Search on Evolving and Static Graphs

In real Web applications, CoSimRank has been proposed as a powerful measure of node-pair similarity based on graph topologies. However, existing work on CoSimRank is restricted to static graphs. When the graph is updated with new edges arriving over time, it is cost-inhibitive to recompute all CoSimRank scores from scratch, which is impractical. In this study, we propose a fast dynamic scheme, \DCoSim for accurate CoSimRank search over evolving graphs. Based on \DCoSim, we also propose a fast scheme, \FCoSim, that greatly accelerates CoSimRank search over static graphs. Our theoretical analysis shows that \DCoSim and \FCoSim guarantee the exactness of CoSimRank scores. On the static graph G, to efficiently retrieve CoSimRank scores \mathbfS , \FCoSim is based on three ideas: (i) It first finds a "spanning polytree»» T over G. (ii) On T, a fast algorithm is designed to compute the CoSimRank scores \mathbfS (T) over the "spanning polytree»» T. (iii) On G, \DCoSim is employed to compute the changes of \mathbfS (T) in response to the delta graph $(G øminus T)$. Experimental evaluations verify the superiority of \DCoSim over evolving graphs, and the fast speedup of \FCoSim on large-scale static graphs against its competitors, without any loss of accuracy

SVS-JOIN : efficient spatial visual similarity join for geo-multimedia

In the big data era, massive amount of multimedia data with geo-tags has been generated and collected by smart devices equipped with mobile communications module and position sensor module. This trend has put forward higher request on large-scale geo-multimedia retrieval. Spatial similarity join is one of the significant problems in the area of spatial database. Previous works focused on spatial textual document search problem, rather than geo-multimedia retrieval. In this paper, we investigate a novel geo-multimedia retrieval paradigm named spatial visual similarity join (SVS-JOIN for short), which aims to search similar geo-image pairs in both aspects of geo-location and visual content. Firstly, the definition of SVS-JOIN is proposed and then we present the geographical similarity and visual similarity measurement. Inspired by the approach for textual similarity join, we develop an algorithm named SVS-JOIN B by combining the PPJOIN algorithm and visual similarity. Besides, an extension of it named SVS-JOIN G is developed, which utilizes spatial grid strategy to improve the search efficiency. To further speed up the search, a novel approach called SVS-JOIN Q is carefully designed, in which a quadtree and a global inverted index are employed. Comprehensive experiments are conducted on two geo-image datasets and the results demonstrate that our solution can address the SVS-JOIN problem effectively and efficiently

More is simpler : effectively and efficiently assessing node-pair similarities based on hyperlinks

Similarity assessment is one of the core tasks in hyperlink analysis. Recently, with the proliferation of applications, e.g., web search and collaborative filtering, SimRank has been a well-studied measure of similarity between two nodes in a graph. It recursively follows the philosophy that "two nodes are similar if they are referenced (have incoming edges) from similar nodes", which can be viewed as an aggregation of similarities based on incoming paths. Despite its popularity, SimRank has an undesirable property, i.e., "zero-similarity": It only accommodates paths with equal length from a common "center" node. Thus, a large portion of other paths are fully ignored. This paper attempts to remedy this issue. (1) We propose and rigorously justify SimRank*, a revised version of SimRank, which resolves such counter-intuitive "zero-similarity" issues while inheriting merits of the basic SimRank philosophy. (2) We show that the series form of SimRank* can be reduced to a fairly succinct and elegant closed form, which looks even simpler than SimRank, yet enriches semantics without suffering from increased computational cost. This leads to a fixed-point iterative paradigm of SimRank* in O(Knm) time on a graph of n nodes and m edges for K iterations, which is comparable to SimRank. (3) To further optimize SimRank* computation, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient and effective heuristic to speed up SimRank* computation to O(Knm) time, where m is generally much smaller than m. (4) Using real and synthetic data, we empirically verify the rich semantics of SimRank*, and demonstrate its high computation efficiency

Co-Simmate : quick retrieving all pairwise co-Simrank scores

Co-Simrank is a useful Simrank-like measure of similarity based on graph structure. The existing method iteratively computes each pair of Co-Simrank score from a dot product of two Pagerank vectors, entailing O(log(1/e)*n^3) time to compute all pairs of Co-Simranks in a graph with n nodes, to attain a desired accuracy e. In this study, we devise a model, Co-Simmate, to speed up the retrieval of all pairs of Co-Simranks to O(log2 (log(1/e))*n^3) time. Moreover, we show the optimality of Co-Simmate among other hop-(u^k) variations, and integrate it with a matrix decomposition based method on singular graphs to attain higher efficiency. The viable experiments verify the superiority of Co-Simmate to others

Sig-SR: SimRank search over singular graphs

SimRank is an attractive structural-context measure of similarity between two objects in a graph. It recursively follows the intuition that "two objects are similar if they are referenced by similar objects". The best known matrix-based method [1] for calculating SimRank, however, implies an assumption that the graph is non-singular, its adjacency matrix is invertible. In reality, non-singular graphs are very rare; such an assumption in [1] is too restrictive in practice. In this paper, we provide a treatment of [1], by supporting similarity assessment on non-invertible adjacency matrices. Assume that a singular graph G has n nodes, with r(2+Kr2)) time for K iterations. In contrast, the only known matrix-based algorithm that supports singular graphs [1] needs O(r4n2) time. The experimental results on real and synthetic datasets demonstrate the superiority of InvSR on singular graphs against its baselines

Fast incremental SimRank on link-evolving graphs

SimRank is an arresting measure of node-pair similarity based on hyperlinks. It iteratively follows the concept that 2 nodes are similar if they are referenced by similar nodes. Real graphs are often large, and links constantly evolve with small changes over time. This paper considers fast incremental computations of SimRank on link-evolving graphs. The prior approach [12] to this issue factorizes the graph via a singular value decomposition (SVD) first, and then incrementally maintains this factorization for link updates at the expense of exactness. Consequently, all node-pair similarities are estimated in O(r4n2) time on a graph of n nodes, where r is the target rank of the low-rank approximation, which is not negligibly small in practice. In this paper, we propose a novel fast incremental paradigm. (1) We characterize the SimRank update matrix ΔS, in response to every link update, via a rank-one Sylvester matrix equation. By virtue of this, we devise a fast incremental algorithm computing similarities of n2 node-pairs in O(Kn2) time for K iterations. (2) We also propose an effective pruning technique capturing the “affected areas” of ΔS to skip unnecessary computations, without loss of exactness. This can further accelerate the incremental SimRank computation to O(K(nd+|AFF|)) time, where d is the average in-degree of the old graph, and |AFF| (≤ n2) is the size of “affected areas” in ΔS, and in practice, |AFF| ≪ n2. Our empirical evaluations verify that our algorithm (a) outperforms the best known link-update algorithm [12], and (b) runs much faster than its batch counterpart when link updates are small

Knowledge Reused Outlier Detection

Tremendous efforts have been invested in the unsupervised outlier detection research, which is conducted on unlabeled data set with abnormality assumptions. With abundant related labeled data available as auxiliary information, we consider transferring the knowledge from the labeled source data to facilitate the unsupervised outlier detection on target data set. To fully make use of the source knowledge, the source data and target data are put together for joint clustering and outlier detection using the source data cluster structure as a constraint. To achieve this, the categorical utility function is employed to regularize the partitions of target data to be consistent with source data labels. With an augmented matrix, the problem is completely solved by a K-means - a based method with the rigid mathematical formulation and theoretical convergence guarantee. We have used four real-world data sets and eight outlier detection methods of different kinds for extensive experiments and comparison. The results demonstrate the effectiveness and significant improvements of the proposed methods in terms of outlier detection and cluster validity metrics. Moreover, the parameter analysis is provided as a practical guide, and noisy source label analysis proves that the proposed method can handle real applications where source labels can be noisy