Graph has been widely used in various applications, while how to optimize the graph is still an open question. In this paper, we propose a framework to optimize the graph structure via structure evolution on graph manifold. We first define the graph manifold and search the best graph structure on this manifold. Concretely, associated with the data features and the prediction results of a given task, we define a graph energy to measure how the graph fits the graph manifold from an initial graph structure. The graph structure then evolves by minimizing the graph energy. In this process, the graph structure can be evolved on the graph manifold corresponding to the update of the prediction results. Alternatively iterating these two processes, both the graph structure and the prediction results can be updated until converge. It achieves the suitable structure for graph learning without searching all hyperparameters. To evaluate the performance of the proposed method, we have conducted experiments on eight datasets and compared with the recent state-of-the-art methods. Experiment results demonstrate that our method outperforms the state-of-the-art methods in both transductive and inductive settings.

Although a number of studies are devoted to novel category discovery, most of them assume a static setting where both labeled and unlabeled data are given at once for finding new categories. In this work, we focus on the application scenarios where unlabeled data are continuously fed into the category discovery system. We refer to it as the {\bf Continuous Category Discovery} ({\bf CCD}) problem, which is significantly more challenging than the static setting. A common challenge faced by novel category discovery is that different sets of features are needed for classification and category discovery: class discriminative features are preferred for classification, while rich and diverse features are more suitable for new category mining. This challenge becomes more severe for dynamic setting as the system is asked to deliver good performance for known classes over time, and at the same time continuously discover new classes from unlabeled data. To address this challenge, we develop a framework of {\bf Grow and Merge} ({\bf GM}) that works by alternating between a growing phase and a merge phase: in the growing phase, it increases the diversity of features through a continuous self-supervised learning for effective category mining, and in the merging phase, it merges the grown model with a static one to ensure satisfying performance for known classes. Our extensive studies verify that the proposed GM framework is significantly more effective than the state-of-the-art approaches for continuous category discovery.