Robust and Scalable Graph-Based Semisupervised Learning

Liu, Wei; Wang, Jun; Chang, Shih-Fu

doi:10.1109/jproc.2012.2197809

Cited by 177 publications

(88 citation statements)

References 39 publications

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“…(3) Extended MNIST: This dataset is widely used in many large-scale graph-based works [14], [19], [24]. The original The best results are shown in bold.…”

Section: Methodsmentioning

confidence: 99%

“…However, since it requires a dense weight matrix to build the relationships between each datapoint and all anchors, its storage requirement becomes impractical for large-scale datasets. Liu et al [23], [24] then presented anchor graph models by constructing the inter-layer edges between datapoints and their nearby anchors. Besides, they also introduced a geometric reconstruction method for their weight estimation to improve its effectiveness.…”

Section: Related Workmentioning

confidence: 99%

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FLAG: Faster Learning on Anchor Graph with Label Predictor Optimization

Wang

Hao

et al. 2022

IEEE Trans. Big Data

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Abstract-Knowledge graphs have received intensive research interests. When the labels of most nodes or datapoints are missing, anchor graph and hierarchical anchor graph models can be employed. With an anchor graph or hierarchical anchor graph, we only need to optimize the labels of the coarsest anchors, and the labels of datapoints can be inferred from these anchors in a coarse-tofine manner. The complexity of optimization is therefore reduced to a cubic cost with respect to the number of the coarsest anchors. However, to obtain a high accuracy when a data distribution is complex, the scale of this anchor set still needs to be large, which thus inevitably incurs an expensive computational burden. As such, a challenge in scaling up these models is how to efficiently estimate the labels of these anchors while keeping classification performance. To address this problem, we propose a novel approach that adds an anchor label predictor in the conventional anchor graph and hierarchical anchor graph models. In the proposed approach, the labels of the coarsest anchors are not directly optimized, and instead, we learn a label predictor which estimates the labels of these anchors with their spectral representations. The predictor is optimized with a regularization on all datapoints based on a hierarchical anchor graph, and we show that its solution only involves the inversion of a small-size matrix. Built upon the anchor hierarchy, we design a sparse intra-layer adjacency matrix over these anchors, which can simultaneously accelerate spectral embedding and enhance effectiveness. Our approach is named Faster Learning on Anchor Graph (FLAG) as it improves conventional anchor-graph-based methods in terms of efficiency. Experiments on a variety of publicly available datasets with sizes varying from thousands to millions of samples demonstrate the effectiveness of our approach.

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“…(3) Extended MNIST: This dataset is widely used in many large-scale graph-based works [14], [19], [24]. The original The best results are shown in bold.…”

Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

FLAG: Faster Learning on Anchor Graph with Label Predictor Optimization

Wang

Hao

et al. 2022

IEEE Trans. Big Data

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“…In this regard, recent experimental results with anchor graphs suggest a way to proceed. In [8] [7][2], the predictive power of non-parametric regression rooted in the anchors/landmarks ensures a way of constructing very informative weighted kNN graphs from a reduced set of representatives (anchors). Since anchor graphs are bipartite (only data-to-anchor edges exist), this representation bridges the sparsity of the pattern space because a random walk traveling from node u to node v must reach one or more anchors in advance.…”

Section: Motivationmentioning

confidence: 99%

Dirichlet Graph Densifiers

Escolano

Curado

Lozano

et al. 2016

Lecture Notes in Computer Science

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Abstract. In this paper, we propose a graph densification method based on minimizing the combinatorial Dirichlet integral for the line graph. This method allows to estimate meaningful commute distances for midsize graphs. It is fully bottom up and unsupervised, whereas anchor graphs, the most popular alternative, are top-down. Compared with anchor graphs, our method is very competitive (it is only outperformed for some choices of the parameters, namely the number of anchors). In addition, although it is not a spectral technique our method is spectrally well conditioned (spectral gap tends to be minimized). Finally, it does not rely on any pre-computation of cluster representatives.

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“…In [6] an approximated kNN is obtained in O(dn t ) with t ∈ (1, 2) by recursively dividing and glueing the samples. More recently, anchor graphs [15] [13] provide data-to-anchor kNN graphs, where m ≪ n is a set of representatives (anchors) typically obtained through K-means clustering, in O(dmnT + dmn) where O(dmnT ) is due to the T iterations of the K-means process. These graphs tend to make out-of-the-sample predictions compatible with those of Nyström approximations, and in turn their approximated adjacency/affinity matrices are ensured to be positive semidefinite.…”

Section: Motivationmentioning

confidence: 99%