Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds
Authors: Yuanyuan Liu, Fanhua Shang, James Cheng, Hong Cheng, Licheng Jiao
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we give a specific iterative scheme for matrix Karcher mean problems, and validate our theoretical results with experiments. In this section, we validate the performance of our accelerated method for averaging SPD matrices under the Riemannian metric, e.g., the matrix Karcher mean problem (9), and also compare our method against the state-of-the-art methods: Riemannian gradient descent (RGD) [31] and limitedmemory Riemannian BFGS (LRBFGS) [29]. |
| Researcher Affiliation | Academia | 1Dept. of Computer Science and Engineering, The Chinese University of Hong Kong 2Dept. of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong 3Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, School of Artificial Intelligence, Xidian University, China |
| Pseudocode | Yes | Algorithm 1 Accelerated method for strongly G-convex optimization and Algorithm 2 Accelerated method for general G-convex optimization |
| Open Source Code | No | The paper does not provide an explicit statement about releasing its source code, nor does it include a link to a code repository. |
| Open Datasets | Yes | The input synthetic data are random SPD matrices of size 100 × 100 or 200 × 200 generated by using the technique in [29] or the matrix mean toolbox [10]... |
| Dataset Splits | No | The paper uses synthetic data for an optimization problem. It does not describe explicit train/validation/test splits, which are more common for supervised learning tasks. It focuses on convergence of the optimization algorithm. |
| Hardware Specification | No | The paper does not provide any specific hardware details (like GPU or CPU models, or cloud computing instance types) used for conducting the experiments. |
| Software Dependencies | No | The paper does not specify software dependencies with version numbers (e.g., specific Python, PyTorch, or TensorFlow versions, or versions of any other libraries used for implementation). |
| Experiment Setup | Yes | The step-size η of both RGD and LRBFGS is selected with a line search method as in [29] (see [29] for details), while η of our accelerated method is set to 1/L. For the algorithms, we initialize X using the arithmetic mean of the data set as in [29]. N is set to 100, and the condition number C of each matrix {Wi}N i=1 is set to 10^2. |