The problem of graph matching (GM) in general is nondeterministic polynomial-complete and many approximate pairwise matching techniques have been proposed. For a general setting in real applications, it typically requires to find the consistent matching across a batch of graphs. Sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence, and the sequences generated in different pairwise matching orders can lead to contradictory solutions. Motivated by devising a robust and consistent multiple-GM model, we propose a unified alternating optimization framework for multi-GM. In addition, we define and use two metrics related to graphwise and pairwise consistencies. The former is used to find an appropriate reference graph, which induces a set of basis variables and launches the iteration procedure. The latter defines the order in which the considered graphs in the iterations are manipulated. We show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix, respectively. Our multi-GM model has two major characters: 1) the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency-driven mechanism and 2) the framework is flexible to incorporate various existing pairwise GM solvers in an out-of-box fashion, and also can proceed with the output of other multi-GM methods. The experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state-of-the-art.

This paper addresses the problem of matching common node correspondences among multiple graphs referring to an identical or related structure. This multi-graph matching problem involves two correlated components: i) the local pairwise matching affinity across pairs of graphs; ii) the global matching consistency that measures the uniqueness of the pairwise matchings by different composition orders. Previous studies typically either enforce the matching consistency constraints in the beginning of an iterative optimization, which may propagate matching error both over iterations and across graph pairs; or separate affinity optimization and consistency enforcement into two steps. This paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function especially when the function is biased due to noises or inappropriate modeling. We propose composition-based multi-graph matching methods to incorporate the two aspects by optimizing the affinity score, meanwhile gradually infusing the consistency. We also propose two mechanisms to elicit the common inliers against outliers. Compelling results on synthetic and real images show the competency of our algorithms.

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Event sequence, asynchronously generated with random timestamp, is ubiquitous among applications. The precise and arbitrary timestamp can carry important clues about the underlying dynamics, and has lent the event data fundamentally different from the time-series whereby series is indexed with fixed and equal time interval. One expressive mathematical tool for modeling event is point process. The intensity functions of many point processes involve two components: the background and the effect by the history. Due to its inherent spontaneousness, the background can be treated as a time series while the other need to handle the history events. In this paper, we model the background by a Recurrent Neural Network (RNN) with its units aligned with time series indexes while the history effect is modeled by another RNN whose units are aligned with asynchronous events to capture the long-range dynamics. The whole model with event type and timestamp prediction output layers can be trained end-to-end. Our approach takes an RNN perspective to point process, and models its background and history effect. For utility, our method allows a black-box treatment for modeling the intensity which is often a pre-defined parametric form in point processes. Meanwhile end-to-end training opens the venue for reusing existing rich techniques in deep network for point process modeling. We apply our model to the predictive maintenance problem using a log dataset by more than 1000 ATMs from a global bank headquartered in North America.