Granular-ball computing (GBC) is an efficient, robust, and scalable learning method for granular computing. The granular ball (GB) generation method is based on GB computing. This article proposes a method for accelerating GB generation using division to replace k -means. It can significantly improve the efficiency of GB generation while ensuring an accuracy similar to that of the existing methods. In addition, a new adaptive method for GB generation is proposed by considering the elimination of the GB overlap and other factors. This makes the GB generation process parameter-free and completely adaptive in the true sense. In addition, this study first provides mathematical models for the GB covering. The experimental results on some real datasets demonstrate that the two proposed GB generation methods have accuracies similar to those of the existing method in most cases, while adaptiveness or acceleration is realized. All the codes were released in the open-source GBC library at https://www.cquptshuyinxia.com/GBC.html or https://github.com/syxiaa/gbc.

This paper presents a strong data-mining method based on a rough set, which can simultaneously realize feature selection, classification, and knowledge representation. Although a rough set, a popular method for feature selection, has good interpretability, it is not sufficiently efficient and accurate to deal with large-scale datasets with high dimensions, which prevents it from being immediately applied to real-world scenarios. To address the efficiency issue of a rough set, we discover the stability of the local redundancy (SLR) of attributes and propose a theorem to prove it rigorously. Based on SLR, only the parts of objects in the boundary region are partitioned when calculating outer significance, which further improves the efficiency of the rough set. With regard to the accuracy issue, we show that overfitting may lead to ineffectiveness of the rough set, especially when processing noise attributes. We then propose relative importance, a robust measurement for an attribute, to alleviate such overfitting issues. In this paper, we propose a novel rough-set framework that significantly improves the efficiency and accuracy of existing rough-set methods. We further develop our rough set framework by proposing a “rough concept tree” for knowledge representation and classification. Experimental results on public benchmark datasets show that our proposed framework achieves higher accuracy than seven state-of-the-art feature-selection methods. All the codes are available athttps://github.com/syxiaa/powerroughset.

Feature selection is an important preprocessing step in data mining and pattern recognition. The neighborhood rough set (NRS) model is a widely-used rough set model for feature selection on continuous data. All currently known NRS models are defined on a distance metric — mostly the euclidean distance metric — which invalidates the NRS models in scenarios wherein the euclidean distance is ineffective, for example, while considering differing attribute weights. We first introduce the concept of space division of granular-rectangular, and then construct the neighborhood radius in our method by describing the relationship between child and parent spaces, which avoids the use of a distance metric and reduces the search space for the neighborhood radius. This greatly improves both the accuracy and efficiency of NRS. In addition, the upper and lower approximations of the granular-rectangular rough sets (GRRSs) comprise equivalence classes; this results in better performance of GRRS in knowledge representation compared with the traditional NRS. Experimental results on public benchmark datasets reveal that our method, GRRS, achieves higher accuracy than ten popular and state-of-the-art feature-selection methods, including two NRS algorithms. Moreover, GRRS outperforms the established NRS algorithms regarding efficiency, including the state-of-the-art NRS algorithm, GBNRS. All code has been released as an open libary called GRRS:https://github.com/syxiaa/GRRS.

Basic Linear Algebra Subprograms (BLAS) serve as a foundational library for scientific computing and machine learning. In this article, we present a new BLAS implementation, FT-BLAS, that provides performance comparable to or faster than state-of-the-art BLAS libraries, while being capable of tolerating soft errors on-the-fly. At the algorithmic level, we propose a hybrid strategy to incorporate fault-tolerant functionality. For memory-bound Level-1 and Level-2 BLAS routines, we duplicate computing instructions and re-use data at the register level to avoid memory overhead when validating the runtime correctness. Here we novelly propose to utilize mask registers on AVX512-enabled processors and SIMD registers on AVX2-enabled processors to store intermediate comparison results. For compute-bound Level-3 BLAS routines, we fuse memory-intensive operations such as checksum encoding and verification into the GEMM assembly kernels to optimize the memory footprint. We also design cache-friendly parallel algorithms for our fault-tolerant library. Through a series of architectural-aware optimizations, we manage to maintain the fault-tolerant overhead at a negligible order ($< $3%). Experimental results obtained on widely-used processors such as Intel Skylake, Intel Cascade Lake, and AMD Zen2 demonstrate that FT-BLAS offers high reliability and high performance – faster than Intel MKL, OpenBLAS, and BLIS by up to 3.50%, 22.14%, and 21.70%, respectively, for both serial and parallel routines spanning all three levels of BLAS we benchmarked, even under hundreds of errors injected per minute.

Integrating recent advancements in resilient algorithms and techniques into existing codes is a singular challenge in fault tolerance - in part due to the underlying complexity of implementing resilience in the first place, but also due to the difficulty introduced when integrating the functionality of a standalone new strategy with the preexisting resilience layers of an application. We propose that the answer is not to build integrated solutions for users, but runtimes designed to integrate into a larger comprehensive resilience system and thereby enable the necessary jump to multi-layered recovery. Our work designs, implements, and verifies one such comprehensive system of runtimes. Utilizing Fenix, a process resilience tool with integration into preexisting resilience systems as a design priority, we update Kokkos Resilience and the use pattern of VeloC to support application-level integration of resilience runtimes. Our work shows that designing integrable systems rather than integrated systems allows for user-designed optimization and upgrading of resilience techniques while maintaining the simplicity and performance of all-in-one resilience solutions. More application-specific choice in resilience strategies allows for better long-term flexibility, performance, and - importantly - simplicity.

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.

Feature reduction is an important aspect of Big Data analytics on today’s ever-larger datasets. Rough sets are a classical method widely applied in attribute reduction. Most rough set algorithms use theprioridomain knowledge of a dataset to process continuous attributes through using a membership function. Neighborhood rough sets (NRS) replace the membership function with the concept of neighborhoods, allowing NRS to handle scenarios where noa prioriknowledge is available. However, the neighborhood radius of each object in NRS is fixed, and the optimization of the radius depends on grid searching. This diminishes both the efficiency and effectiveness, leading to a time complexity of not lower than$O(N^2)$O(N2). To resolve these limitations, granular ball neighborhood rough sets (GBNRS), a novel NRS method with time complexity$O(N)$O(N), is proposed. GBNRS adaptively generates a different neighborhood for each object, resulting in greater generality and flexibility in comparison to standard NRS methods. GBNRS is compared with the current state-of-the-art NRS method, FARNeMF, and find that GBNRS obtains both higher performance and higher classification accuracy on public benchmark datasets. All code has been released in the open source GBNRS library athttp://www.cquptshuyinxia.com/GBNRS.html.

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.

Basic Linear Algebra Subprograms (BLAS) is a core library in scientific computing and machine learning. This paper presents FT-BLAS, a new implementation of BLAS routines that not only tolerates soft errors on the fly, but also provides comparable performance to modern state-of-the-art BLAS libraries on widely-used processors such as Intel Skylake and Cascade Lake. To accommodate the features of BLAS, which contains both memory-bound and computing-bound routines, we propose a hybrid strategy to incorporate fault tolerance into our brand-new BLAS implementation: duplicating computing instructions for memory-bound Level-1 and Level-2 BLAS routines and incorporating an Algorithm-Based Fault Tolerance mechanism for computing-bound Level-3 BLAS routines. Our high performance and low overhead are obtained from delicate assembly-level optimization and a kernel-fusion approach to the computing kernels. Experimental results demonstrate that FT-BLAS offers high reliability and high performance -- faster than Intel MKL, OpenBLAS, and BLIS by up to 3.50%, 22.14% and 21.70%, respectively, for routines spanning all three levels of BLAS we benchmarked, even under hundreds of errors injected per minute.

Introspective sorting is a ubiquitous sorting algorithm which underlies many large scale distributed systems. Hardware-mediated soft errors can result in comparison and memory errors, and thus cause introsort to generate incorrect output, which in turn disrupts systems built upon introsort; hence, it is critical to incorporate fault tolerance capability within introsort. This paper proposes the first theoretically-sound, practical fault tolerant introsort with negligible overhead: FT-iSort. To tolerate comparison errors, we use minimal TMR protection via exploiting the properties of the effects of soft errors on introsort. This algorithm-based selective protection incurs far less overhead than naïve TMR protection designed to protect an entire application. To tolerate memory errors that escape DRAM error correcting code, we propose XOR-based re-execution. We incorporate our fault tolerance method into the well-known parallel sorting implementation HykSort, and we find that fault tolerant HykSort incurs negligible overhead and obtains nearly the same scalability as unprotected HykSort.