Online change-point detection (OCPD) is important for application in various areas such as finance, biology, and the Internet of Things (IoT). However, OCPD faces major challenges due to high-dimensionality, and it is still rarely studied in literature. In this paper, we propose a novel, online, graph-based, change-point detection algorithm to detect change of distribution in low- to high-dimensional data. We introduce a similarity measure, which is derived from the graph-spanning ratio, to test statistically if a change occurs. Through numerical study using artificial online datasets, our data-driven approach demonstrates high detection power for high-dimensional data, while the false alarm rate (type I error) is controlled at a nominal significant level. In particular, our graph-spanning approach has desirable power with small and multiple scanning window, which allows timely detection of change-point in the online setting.
Graph-based CPD methods are two-sample tests based on various types of graphs representing the similarity between observations, which are first proposed by Friedman and Rafsky @cite_4 (1979) using minimum-spanning tree (MST) graph. Also, Rosenbaum @cite_10 (2005) propose another test based on the minimum-distance pairing (MDP) using the rank of the distance within the pairs, which is thus restricted to MDP graph. Recently, Chen and Zhang @cite_2 (2015), utilize MST and MDP graph representations onto the data, and construct a test statistic based on counting the number of edges connecting points from different groups. They demonstrate that graph-based CPD has better detection power at high-dimensional data compared to parametric methods, such as Hotelling’s @math and generalized likelihood ratio test. Chen and Zheng develop an algorithm to count the edges between groups before and after the potential change-point. However, this pioneer CPD graph method, firstly, works only for offline detection, which is not sufficient in fields where an immediate reaction is needed when a change-point is detected. Secondly, its detection power is comparably not sensible to the variance change and is limited by the size of the dataset. Our proposed method contributes in filling the aforementioned gaps.
@cite_10 @cite_4 @cite_2
2097746044 2169357279 2964204618 2807333821
In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics and relate it to the problem of finding a sparsest cut in a graph. We develop a tractable relaxation of the GLR statistic based on the combinatorial Laplacian of the graph, which we call the spectral scan statistic, and analyze its properties. We show how its performance as a testing procedure depends directly on the spectrum of the graph, and use this result to explicitly derive its asymptotic properties on few significant graph topologies. Finally, we demonstrate both theoretically and by simulations that the spectral scan statistic can outperform naive testing procedures based on edge thresholding and @math testing. This paper deals with active sampling of graph nodes representing training data for binary classification. The graph may be given or constructed using similarity measures among nodal features. Leveraging the graph for classification builds on the premise that labels across neighboring nodes are correlated according to a categorical Markov random field (MRF). This model is further relaxed to a Gaussian (G)MRF with labels taking continuous values—an approximation that not only mitigates the combinatorial complexity of the categorical model, but also offers optimal unbiased soft predictors of the unlabeled nodes. The proposed sampling strategy is based on querying the node whose label disclosure is expected to inflict the largest change on the GMRF, and in this sense it is the most informative on average. Connections are established to other sampling methods including uncertainty sampling, variance minimization, and sampling based on the @math optimality criterion. A simple yet effective heuristic is also introduced for increasing the exploration capabilities of the sampler, and reducing bias of the resultant classifier, by adjusting the confidence on the model label predictions. The novel sampling strategies are based on quantities that are readily available without the need for model retraining, rendering them computationally efficient and scalable to large graphs. Numerical tests using synthetic and real data demonstrate that the proposed methods achieve accuracy that is comparable or superior to the state of the art even at reduced runtime. Abstract We present a novel convolutional neural network (CNN) based pipeline which can effectively fuse multi-level information extracted from different intermediate layers generating hybrid convolutional features (HCF) for edge detection. Different from previous methods, the proposed method fuses multi-level information in a feature-map based manner. The produced hybrid convolutional features can be used to perform high-quality edge detection. The edge detector is also computationally efficient, because it detects edges in an image-to-image way without any post-processing. We evaluate the proposed method on three widely used datasets for edge detection including BSDS500, NYUD and Multicue, and also test the method on Pascal VOC’12 dataset for object contour detection. The results show that HCF achieves an improvement in performance over the state-of-the-art methods on all four datasets. On BSDS500 dataset, the efficient version of the proposed approach achieves ODS F-score of 0.804 with a speed of 22 fps and the high-accuracy version achieves ODS F-score of 0.814 with 11 fps .