Learning on Big Graph: Label Inference and Regularization with Anchor Hierarchy

Wang, Meng; Fu, Weijie; Hao, Shijie; Liu, Hengchang; Wu, Xindong

doi:10.1109/tkde.2017.2654445

Cited by 117 publications

(38 citation statements)

References 33 publications

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“…For example, Zhang et al [49] employed Locality-Sensitive Hashing into the graph construction. Wang et al [41] introduced a treebased ANNS algorithm [30] to accelerate their weight estimation.…”

Section: Related Workmentioning

confidence: 99%

“…As a consequence, the computational costs of the geometric reconstruction and the model optimization can be expensive. Wang et al [41] therefore extended anchor graph models into a pyramidstyle structure by exploring multiple anchor sets, which can improve the classification accuracy by introducing a finer anchor set while fixing the size of the coarsest anchor set. As a result, it carries out hierarchical label inference from the coarsest anchors in a coarse-to-fine manner, and its optimization only involves the inversion of a matrix with the size of the coarsest anchor set.…”

Section: Related Workmentioning

confidence: 99%

“…As pointed in [41], this adjacency matrix naturally introduces adaptive inter-layer adjacency relationships between each datapoint and its nearby coarsest anchors.…”

Section: Anchor-graph-based Learningmentioning

confidence: 99%

“…To deal with a standard multi-class SSL problem, Hierarchical Anchor Graph Regularization (HAGR) [41] is formulated by minimizing the following problem: …”

Section: Anchor-graph-based Learningmentioning

confidence: 99%

“…Recently, a hierarchical anchor graph model with a pyramid-style structure is proposed in [41], which explores multiple-layer anchors to perform hierarchical label inference layer by layer. As a result, this approach can enlarge its finest anchor layer to improve classification performance.…”

Section: Introductionmentioning

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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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…As pointed in [41], this adjacency matrix naturally introduces adaptive inter-layer adjacency relationships between each datapoint and its nearby coarsest anchors.…”

Section: Anchor-graph-based Learningmentioning

confidence: 99%

“…To deal with a standard multi-class SSL problem, Hierarchical Anchor Graph Regularization (HAGR) [41] is formulated by minimizing the following problem: …”

Section: Anchor-graph-based Learningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations