Density peaks clustering (DP) has the ability of detecting clusters of arbitrary shape and clustering non-Euclidean space data, but its quadratic complexity in both computing and storage makes it difficult to scale for big data. Various approaches have been proposed in this regard, including MapReduce based distribution computing, multi-core parallelism, presentation transformation (e.g., kd-tree, Z-value), granular computing, and so forth. However, most of these existing methods face two limitations. One is their target datasets are mostly constrained to be in Euclidian space, the other is they emphasize only on local neighbors while ignoring global data distribution due to restriction to cut-off kernel when computing density. To address the two issues, we present a faithful and parallel DP method that makes use of two types of vector-like distance matrices and an inverse leading-node-finding policy. The method is implemented on a message passing interface (MPI) system. Extensive experiments showed that our method is capable of clustering non-Euclidean data such as in community detection, while outperforming the state-of-the-art counterpart methods in accuracy when clustering large Euclidean data. Our code is publicly available at https://github.com/alanxuji/FaithPDP.

Long-tailed (LT) classification is an unavoidable and challenging problem in the real world. Most existing long-tailed classification methods focus only on solving the class-wise imbalance while ignoring the attribute-wise imbalance. The deviation of a classification model is caused by both class-wise and attribute-wise imbalance. Due to the fact that attributes are implicit in most datasets and the combination of attributes is complex, attribute-wise imbalance is more difficult to handle. For this purpose, we proposed a novel long-tailed classification framework, aiming to build a multi-granularity classification model by means of invariant feature learning. This method first unsupervisedly constructs Coarse-Grained forest (CLF) to better characterize the distribution of attributes within a class. Depending on the distribution of attributes, one can customize suitable sampling strategies to construct different imbalanced datasets. We then introduce multi-center loss (MCL) that aims to gradually eliminate confusing attributes during feature learning process. The proposed framework does not necessarily couple to a specific LT classification model structure and can be integrated with any existing LT method as an independent component. Extensive experiments show that our approach achieves state-of-the-art performance on both existing benchmarks ImageNet-GLT and MSCOCO-GLT and can improve the performance of existing LT methods. Our codes are available on GitHub: \url{https://github.com/jinyery/cognisance}