graph kernel from data features via distance metric learning that characterizes pairwise similarities of data. We deploy the *Mahalanobis distance* [@mahalanobis1936], which takes into account data correlations for intrinsic representation. Given a K-dimensional feature vector $\mathbf{f}_i$ per node $i$, $\mathbf{f}_i \in \mathbb{R}^K$, the Mahalanobis distance between the features $\mathbf{f}_i$ and $\mathbf{f}_j$ of nodes $i$ and $j$ is defined as: $d_{\mathbf{M}}(\mathbf{f}_i,\mathbf{f}_j)=\sqrt{(\mathbf{f}_i - \mathbf{f}_j)^{\top} \mathbf{M} (\mathbf{f}_i - \mathbf{f}_j)}$, where $\mathbf{M} \in \mathbb{R}^{K \times K}$ is the Mahalanobis distance metric matrix which reflects feature correlations. Hence, we convert the problem of graph learning to the optimization of $\mathbf{M}$. As $\mathbf{M}$ is positive semi-definite (PSD), it is often nontrivial to solve efficiently. Instead, we decompose it as $\mathbf{M} = \mathbf{R} \mathbf{R}^{\top}$ and learn $\mathbf{R}$ for ease of optimization, where $\mathbf{R} \in \mathbb{R}^{K \times S}$ has a lower dimension $S<<K$ to reduce number of parameters for efficient implementation. Given features $\mathbf{f}$, we seek to minimize the Graph Laplacian Regularizer (GLR) [@shuman2013emerging] $\mathbf{f}^{\top}\mathbf{L}(\mathbf{R})\mathbf{f}$ by optimizing $\mathbf{R}$, which measures the smoothness of features $\mathbf{f}$ with respect to the graph Laplacian $\mathbf{L}$[^1]. This essentially enforces the graph encoded in $\mathbf{L}(\mathbf{R})$ to capture pairwise similarities of $\mathbf{f}$. Hence, we formulate the joint learning of graphs $\mathbf{L}(\mathbf{R})$ and node features 