Recent years have witnessed the superiority of non-convex s parse learning formulations over their convex counterparts in both theory and pr actice. However, due to the non-convexity and non-smoothness of the regularizer, how to efficiently solve the non-convex optimization problem for large-scale data is still quite challenging. In this paper, we propose an efficient H ybrid O ptimization algorithm for NO n-convex R egularized problems (HONOR). Specifically, we develop a hybrid scheme which effectively integrates a Quasi-Newton (Q N) step and a Gradient Descent (GD) step. Our contributions are as follows: ( 1) HONOR incorporates the second-order information to greatly speed up th e convergence, while it avoids solving a regularized quadratic programming and o nly involves matrix-vector multiplications without explicitly forming the inv erse Hessian matrix.

This approach yields biased estimates of the expected risk, and therefore leads to poor decisions for two reasons.

Neural Information Processing Systems http://nips.cc/

Table 1 reports the results of a controlled experiment evaluating different components in our framework for auxiliary label generation. Positive correspondences are generated by matching pixels across different augmentations of the same image. With respect to the clustering algorithm, K-means performs better than DBSCAN (#4 vs. #5), which is We show qualitative results, comparing different feature extractors in Figure 1. DBSCAN is limited by the memory and computational complexity. Corresponding qualitative results are shown in Figure 3. Tables 3-5 show We observe the best performance when 5% outliers are removed.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Graph-based algorithms are among the most successful paradigms for solving semi-supervised learning tasks.