GBRS: A Unified Granular-Ball Learning Model of Pawlak Rough Set and Neighborhood Rough Set.

Pawlak rough set (PRS) and neighborhood rough set (NRS) are the two most common rough set theoretical models. Although the PRS can use equivalence classes to represent knowledge, it is unable to process continuous data. On the other hand, NRSs, which can process continuous data, rather lose the ability of using equivalence classes to represent knowledge. To remedy this deficit, this article presents a granular-ball rough set (GBRS) based on the granular-ball computing combining the robustness and the adaptability of the granular-ball computing. The GBRS can simultaneously represent both the PRS and the NRS, enabling it not only to be able to deal with continuous data and to use equivalence classes for knowledge representation as well. In addition, we propose an implementation algorithm of the GBRS by introducing the positive region of GBRS into the PRS framework. The experimental results on benchmark datasets demonstrate that the learning accuracy of the GBRS has been significantly improved compared with the PRS and the traditional NRS. The GBRS also outperforms nine popular or the state-of-the-art feature selection methods. We have open-sourced all the source codes of this article at http://www.cquptshuyinxia.com/GBRS.html, https://github.com/syxiaa/GBRS.

Toward Feature-Preserving Vector Field Compression.

The objective of this work is to develop error-bounded lossy compression methods to preserve topological features in 2D and 3D vector fields. Specifically, we explore the preservation of critical points in piecewise linear and bilinear vector fields. We define the preservation of critical points as, without any false positive, false negative, or false type in the decompressed data, (1) keeping each critical point in its original cell and (2) retaining the type of each critical point (e.g., saddle and attracting node). The key to our method is to adapt a vertex-wise error bound for each grid point and to compress input data together with the error bound field using a modified lossy compressor. Our compression algorithm can be also embarrassingly parallelized for large data handling and in situ processing. We benchmark our method by comparing it with existing lossy compressors in terms of false positive/negative/type rates, compression ratio, and various vector field visualizations with several scientific applications.

mCRF and mRD: Two Classification Methods Based on a Novel Multiclass Label Noise Filtering Learning Framework.

Mitigating label noise is a crucial problem in classification. Noise filtering is an effective method of dealing with label noise which does not need to estimate the noise rate or rely on any loss function. However, most filtering methods focus mainly on binary classification, leaving the more difficult counterpart problem of multiclass classification relatively unexplored. To remedy this deficit, we present a definition for label noise in a multiclass setting and propose a general framework for a novel label noise filtering learning method for multiclass classification. Two examples of noise filtering methods for multiclass classification, multiclass complete random forest (mCRF) and multiclass relative density, are derived from their binary counterparts using our proposed framework. In addition, to optimize the NI_threshold hyperparameter in mCRF, we propose two new optimization methods: a new voting cross-validation method and an adaptive method that employs a 2-means clustering algorithm. Furthermore, we incorporate SMOTE into our label noise filtering learning framework to handle the ubiquitous problem of imbalanced data in multiclass classification. We report experiments on both synthetic data sets and UCI benchmarks to demonstrate our proposed methods are highly robust to label noise in comparison with state-of-the-art baselines. All code and data results are available at https://github.com/syxiaa/Multiclass-Label-Noise-Filtering-Learning.

Ball k-Means: Fast Adaptive Clustering With No Bounds.

This paper presents a novel accelerated exact k-means called as "Ball k-means" by using the ball to describe each cluster, which focus on reducing the point-centroid distance computation. The "Ball k-means" can exactly find its neighbor clusters for each cluster, resulting distance computations only between a point and its neighbor clusters' centroids instead of all centroids. What's more, each cluster can be divided into "stable area" and "active area", and the latter one is further divided into some exact "annular area". The assignment of the points in the "stable area" is not changed while the points in each "annular area" will be adjusted within a few neighbor clusters. There are no upper or lower bounds in the whole process. Moreover, ball k-means uses ball clusters and neighbor searching along with multiple novel stratagems for reducing centroid distance computations. In comparison with the current state-of-the art accelerated exact bounded methods, the Yinyang algorithm and the Exponion algorithm, as well as other top-of-the-line tree-based and bounded methods, the ball k-means attains both higher performance and performs fewer distance calculations, especially for large-k problems. The faster speed, no extra parameters and simpler design of "Ball k-means" make it an all-around replacement of the naive k-means.

Random Space Division Sampling for Label-Noisy Classification or Imbalanced Classification.

This article presents a simple sampling method, which is very easy to be implemented, for classification by introducing the idea of random space division, called "random space division sampling" (RSDS). It can extract the boundary points as the sampled result by efficiently distinguishing the label noise points, inner points, and boundary points. This makes it the first general sampling method for classification that not only can reduce the data size but also enhance the classification accuracy of a classifier, especially in the label-noisy classification. The "general" means that it is not restricted to any specific classifiers or datasets (regardless of whether a dataset is linear or not). Furthermore, the RSDS can online accelerate most classifiers because of its lower time complexity than most classifiers. Moreover, the RSDS can be used as an undersampling method for imbalanced classification. The experimental results on benchmark datasets demonstrate its effectiveness and efficiency. The code of the RSDS and comparison algorithms is available at: https://github.com/syxiaa/RSDS.

Double conductivity-improved porous Sn/Sn4P3@carbon nanocomposite as high performance anode in Lithium-ion batteries.

Carbon encapsulated porous Sn/Sn4P3 (Sn/Sn4P3@C) composite is conveniently prepared by one-step electrochemical dealloying of Sn80P20 alloy in mild conditions followed by growing one carbon layer. Controllable dealloying of the Sn80P20 alloy results in the formation of bicontinuous spongy Sn4P3 nanostructure with a part of residued metallic Sn atoms embedded in the porous skeleton. A uniform carbon layer is deposited on the nanoporous Sn/Sn4P3 to prevent the nanostructure's pulverizing and agglomerating during lithium ion insertion/extraction. Upon double conductivity modification from metallic Sn matrix and carbon layer, the as-made composite displays superior lithium-storage performances with much higher specific capacity as well as better cycling stability compared with pure porous Sn4P3. It offers a specific capacity of 837 mA h g-1 after 100 cycles at a rate of 100 mA g-1. Even after 700 cycles at the higher rate of 1000 mA g-1, the specific capacity still maintains as high as 589 mA h g-1. The Sn/Sn4P3@C material possesses promising application potential as an alternative anode in the lithium storage fields.

One-step mild fabrication of porous core-shelled Si@TiO2 nanocomposite as high performance anode for Li-ion batteries.

Nanoporous Si@TiO2 composites with the unique core-shell architecture are conveniently fabricated through one-step selective dealloying of SiTiAl ternary alloy under mild conditions. The as-prepared composites consist of bimodal Si network skeleton as the core and interconnected TiO2 nanosponge layer as the shell uniformly distribute on the Si surface to form the porous core-shelled structure. The nanoporous TiO2 as the outer protective layer not only reduce the violent volume change of electrode materials for stable cycling performance but also shorten the diffusion distance of Li+ for high rate capacities. The inner bimodal porous Si possesses an open bicontinuous network structure that can provide the enough empty space and robust backbone to relax the volume variation of composite and guarantee the sufficient electrode-electrolyte contact area. As a result, the optimized nanoporous Si@TiO2 composite delivers the reversible capacity of 1338.1 and 1174.4 mA h g-1 at the current densities of 200 and 1000 mA g-1 after continuous tests for 120 and 100 cycles, respectively. With the advantages of easy preparation, unique architecture, and high lithium storage performances, the porous core-shelled Si@TiO2 composites demonstrate the promising application potential as an anode material for LIBs.

Tin sulphide nanoflowers anchored on three-dimensional porous graphene networks as high-performance anode for sodium-ion batteries.

The SnS2 nanoflowers anchored on three dimensional porous graphene were easily constructed with nickel foam (NF) as supported backbone through the dip-coating method followed by one-step controllable hydrothermal growth and mild reduction. The interconnected SnS2 nanoflowers with cross-linking nanosheets and rich pores assembled to form one layer of continuous network structure, which tightly adhered on the surface of graphene. The porous graphene supported by NF built a conductively integral highway that is preferable for the charge transfer kinetics, while the hierarchical pores from the SnS2 nanoflowers and NF are particularly beneficial for mitigating the volume expansion and promoting electrolyte penetration. The as-constructed Ni foam/reduced graphene oxide/SnS2 (NF/RGO/SnS2) composite exhibited dramatically enhanced reversible capacity, remarkable rate capability, and long-term cycling stabilities without the use of any binders and conductive additives. Especially, NF/RGO/SnS2 composite remained the specific capacity as high as 561.9 mA h g-1 at the current densities of 1000 mA g-1 after continuous tests for 160 cycles, which is much higher than conventional SnS2/RGO composite. With the advantages of unique architecture and excellent sodium storage performances, the NF/RGO/SnS2 composite shows promising application potential in the sodium ion batteries.