Metric learning, aiming to learn a discriminative Mahalanobis distance matrix M that can effectively reflect the similarity between data samples, has been widely studied in various image recognition problems. Most of the existing metric learning methods input the features extracted directly from the original data in the preprocess phase. What's worse, these features usually take no consideration of the local geometrical structure of the data and the noise existed in the data, thus they may not be optimal for the subsequent metric learning task. In this paper, we integrate both feature extraction and metric learning into one joint optimization framework and propose a new bilevel distance metric learning model. Specifically, the lower level characterizes the intrinsic data structure using graph regularized sparse coefficients, while the upper level forces the data samples from the same class to be close to each other and pushes those from different classes far away. In addition, leveraging the KKT conditions and the alternating direction method (ADM), we derive an efficient algorithm to solve the proposed new model. Extensive experiments on various occluded datasets demonstrate the effectiveness and robustness of our method.

Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds.

The croissant metadata record is available at croissant. We chose GitHub and Google Drive respectively to store our code and dataset. Both are widely recognized as reliable data storage platforms, ensuring long-term preservation. We highly recommend downloading the raw data directly and following the provided instructions to simplify the data processing steps. Our dataset is structured as follows: the local directory contains client-specific data for local training, while all clients aggregates data from all clients for federated learning.

D.9 Parameter Size and Inference Speed . . . . . . . . . . . . . . . . . . . . . . . .