for different individuals. Spatio-temporal graph routing (STGR) is proposed [@li2019spatio] to learn one spatial graph and one temporal graph for each skeleton instance. Adaptive graph convolution network (AGCN) is proposed [@li2018adaptive] to construct a unique residual Laplacian matrix by learning Mahalanobis distance metric for each instance. Different from the task-driven AGCN where the Mahalanobis distance metric $\mathbf{M}$ is learned by minimizing the cross-entropy only, we optimize $\mathbf{M}$ via both the GLR and cross-entropy. Also, we assume $\mathbf{M}$ is low rank and set $S << K$ to reduce number of parameters while AGCN adopts $S = K$;

### Hybrid Graph Learning

For special applications like skeleton-based action recognition, both fixed-domain and varying-domain graph learning can be applied according to the way of graph construction. NLGCN [@shi2018non] builds three graphs for each instance: the pre-defined physical skeleton graph, a shared graph for all instances, and an individual graph learned from each instance’s own feature in a non-local [@wang2018non] manner.

Background in Spectral Graph Theory {#sec:graph}
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Graph and Graph Laplacian
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An undirected graph $\mathcal{G}=\{\mathcal{V},\mathcal{E},\mathbf{A}\}$ is composed of a vertex set $\mathcal{V}$ of cardinality $\left|\mathcal{V}\right|=N$, an edge set $\mathcal{E}$ connecting vertices, and a weighted adjacency matrix $\mathbf{A}$. $\mathbf{A} \in \mathbb{R}^{N \times N}$ 