Research Work

Current Work

Graph Convolutional Networks (GCN)

Similar to the CNN applied on the image classification problem, GCN take the information of neighbors into node embedding.

\[ \begin{align*} \tilde{\vec{A}} &= \vec{A} + \vec{I}, \tilde{\vec{D}} = \vec{D} + \vec{I}\\ \hat{\vec{A}} &= \tilde{\vec{D}}^{-1/2} \tilde{\vec{A}} \tilde{\vec{D}}^{-1/2}\\ \vec{H}^{(l+1)} &= \sigma(\hat{\vec{A}} \vec{H}^{(l)} \vec{W}^{(l)}) \end{align*} \]

• robust GCN

• adversarial training of GCN

• representation learnings

• etc.

Applications

• node classification, link prediction, recommendation systems, protein-protein interactions, Drug-testing and etc.

Previous work

Newton-type optimization using Cubic Regularization

\[ \begin{align} \label{eq:cd} q(\vec{u}) = \vec{g}^\top \vec{u} + \frac{1}{2}\vec{u}^\top \vec{H} \vec{u} + \frac{L}{6}\norm{\vec{u}}^3 \end{align} \]

The cubic approximation function \(\eqref{eq:cd}\) is called cubic regularization. It is related to other optimization method like gradient descent, trust-region method.

Other topics

Gradient descent optimization

Taking the negation of gradients as the descent directions.

Coordinate descent optimization

Successively minimize along coordinate directions to find the minimum of a function.