Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.
Previous graph matching affinity learning methods are mostly based on simple and shallow parametric models, which use popular distances (typically weighted Euclid distance) in the node and edge feature space plus a similarity kernel function (e.g. Gaussian kernel) to derive the final affinity score. In particular, a unified (shallow) parametric graph structure learning model is devised between two graphs in a vector form @math @cite_30 . The authors in @cite_30 observe that the above simple model can incorporate most previous shallow learning models, including @cite_43 @cite_16 @cite_12 . Therefore, this method will be compared in our experiment.
@cite_30 @cite_43 @cite_16 @cite_12
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A novel homogeneity-based method for music structure analysis is proposed. The heart of the method is a similarity measure, derived from first principles, that is based on the matrix Elastic Net (EN) regularization and deals efficiently with highly correlated audio feature vectors. In particular, beat-synchronous mel-frequency cepstral coefficients, chroma features, and auditory temporal modulations model the audio signal. The EN induced similarity measure is employed to construct an affinity matrix, yielding a novel subspace clustering method referred to as Elastic Net subspace clustering (ENSC). The performance of the ENSC in structure analysis is assessed by conducting extensive experiments on the Beatles dataset. The experimental findings demonstrate the descriptive power of the EN-based affinity matrix over the affinity matrices employed in subspace clustering methods, attaining the state-of-the-art performance reported for the Beatles dataset. In this letter, we propose a novel low-rank-represen-tation (LRR) based manifold-regularization approach for zero-shot learning (ZSL). Most existing regularization-based ZSL approaches perform the alignment between visual feature space and semantic space based on the affinity matrix constructed from the test instances. The affinity matrix plays a significant role in exploiting the manifold structures of visual feature space, hence we propose to use the LRR to guide the affinity-matrix construction by exploring the subspace structures of data. Considering the locality and similarity information among data, we incorporate a Laplacian regularization term to the LRR framework to ensure that the learned affinity matrix can capture the local geometric structures in data. We also explicitly impose the nonnegative sparse constraint on the affinity matrix to facilitate the learning of local manifold structures. Moreover, we use an effective manifold-regularization methodology to learn discriminative semantic representations of test instances, leading to significant improvements in classification performance over the unseen classes. Extensive experiments on three benchmark datasets demonstrate that the proposed approach outperforms the state of the arts. Previous experiments with low dimensional data sets have shown that Gabriel graph methods for instance-based learning are among the best machine learning algorithms for pattern classification applications. However, as the dimensionality of the data grows large, all data points in the training set tend to become Gabriel neighbors of each other, bringing the efficacy of this method into question. Indeed, it has been conjectured that for high-dimensional data, proximity graph methods that use sparser graphs, such as relative neighbor graphs (RNG) and minimum spanning trees (MST) would have to be employed in order to maintain their privileged status. Here the performance of proximity graph methods, in instance-based learning, that employ Gabriel graphs, relative neighborhood graphs, and minimum spanning trees, are compared experimentally on high-dimensional data sets. These methods are also compared empirically against the traditional k-NN rule and support vector machines (SVMs), the leading competitors of proximity graph methods. Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NP-hard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more general problem of matching N attributed graphs to each other, i.e. labeling their common node correspondences such that a certain compatibility affinity objective is optimized. This multi-graph matching problem involves two key ingredients affecting the overall accuracy: a) the pairwise affinity matching score between two local graphs, and b) global matching consistency that measures the uniqueness and consistency of the pairwise matching results by different sequential matching orders. Previous work typically either enforces the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across different graph pairs; or separates score optimizing and consistency synchronization in two steps. This paper is motivated by the observation that affinity score and consistency are mutually affected and shall be tackled jointly to capture their correlation behavior. As such, we propose a novel multi-graph matching algorithm to incorporate the two aspects by iteratively approximating the global-optimal affinity score, meanwhile gradually infusing the consistency as a regularizer, which improves the performance of the initial solutions obtained by existing pairwise graph matching solvers. The proposed algorithm with a theoretically proven convergence shows notable efficacy on both synthetic and public image datasets.