Active Sample Selection Based Incremental Algorithm for Attribute Reduction with Rough Sets

Attribute reduction with rough sets is an effective technique for obtaining a compact and informative attribute set from a given dataset. However, traditional algorithms have no explicit provision for handling dynamic datasets where data present themselves in successive samples. Incremental algorithms for attribute reduction with rough sets have been recently introduced to handle dynamic datasets with large samples, though they have high complexity in time and space. To address the time/space complexity issue of the algorithms, this paper presents a novel incremental algorithm for attribute reduction with rough sets based on the adoption of an active sample selection process and an insight into the attribute reduction process. This algorithm first decides whether each incoming sample is useful with respect to the current dataset by the active sample selection process. A useless sample is discarded while a useful sample is selected to update a reduct. At the arrival of a useful sample, the attribute reduction process is then employed to guide how to add and/or delete attributes in the current reduct. The two processes thus constitute the theoretical framework of our algorithm. The proposed algorithm is finally experimentally shown to be efficient in time and space

Parameterized Local Reduction of Decision Systems

One important and valuable topic in rough sets is attribute reduction of a decision system. The existing attribute reductions are designed to just keep confidence of every certain rule as they cannot identify key conditional attributes explicitly for special decision rules. In this paper, we develop the concept of -local reduction in order to offer a minimal description for special -possible decision rules. The approach of discernibility matrix is employed to investigate the structure of a -local reduction and compute all -local reductions. An example of medical diagnosis is employed to illustrate our idea of the -local reduction. Finally, numerical experiments are performed to show that our method proposed in this paper is feasible and valid

Reduction method based on a new fuzzy rough set in fuzzy information system and its applications to scheduling problems

AbstractIn this paper, we present the concept of fuzzy information granule based on a relatively weaker fuzzy similarity relation called fuzzy TL-similarity relation for the first time. Then, according to the fuzzy information granule, we define the lower and upper approximations of fuzzy sets and a corresponding new fuzzy rough set. Furthermore, we construct a kind of new fuzzy information system based on the fuzzy TL-similarity relation and study its reduction using the fuzzy rough set. At last, we apply the reduction method based on the defined fuzzy rough set in the above fuzzy information system to the reduction of the redundant multiple fuzzy rule in the scheduling problems, and numerical computational results show that the reduction method based on the new fuzzy rough set is more suitable for the reduction of multiple fuzzy rules in the scheduling problems compared with the reduction methods based on the existing fuzzy rough set

Charge Modulations in the Superconducting State of the Cuprates

Motivated by the recent scanning tunneling microscopy (STM) and neutron scattering experiments, we investigate various charge density wave orders coexisting with superconductivity in the cuprate superconductors. The explicit expressions of the local density of states and its Fourier component at the ordering wavevector for the weak charge modulations are derived. It is shown that the STM experiments in $Bi_2Sr_2CaCu_2O_{8+\delta}$ cannot be explained by a site- or bond-centered charge modulation alone, but agree well with the presence of the dimerization hopping and transverse pairing modulations. We also calculate the spectral function for the charged stripes, which is measured by the ARPES experiments.Comment: 3 pages with 4 figures. To be published in PR

Harmonic and power balance tools for tapping-mode atomic force microscope

The atomic force microscope(AFM) is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever–sample interaction is developed. The energy dissipation in the sample is studied and the resulting power balance equations combined with the harmonic balance equations are used to estimate the model parameters. Experimental results confirm that the harmonic and power balance tools can be used effectively to predict the behavior of the tapping cantilever

RFAConv: Innovating Spatital Attention and Standard Convolutional Operation

Spatial attention has been widely used to improve the performance of convolutional neural networks by allowing them to focus on important information. However, it has certain limitations. In this paper, we propose a new perspective on the effectiveness of spatial attention, which is that it can solve the problem of convolutional kernel parameter sharing. Despite this, the information contained in the attention map generated by spatial attention is not sufficient for large-size convolutional kernels. Therefore, we introduce a new attention mechanism called Receptive-Field Attention (RFA). While previous attention mechanisms such as the Convolutional Block Attention Module (CBAM) and Coordinate Attention (CA) only focus on spatial features, they cannot fully address the issue of convolutional kernel parameter sharing. In contrast, RFA not only focuses on the receptive-field spatial feature but also provides effective attention weights for large-size convolutional kernels. The Receptive-Field Attention convolutional operation (RFAConv), developed by RFA, represents a new approach to replace the standard convolution operation. It offers nearly negligible increment of computational cost and parameters, while significantly improving network performance. We conducted a series of experiments on ImageNet-1k, MS COCO, and VOC datasets, which demonstrated the superiority of our approach in various tasks including classification, object detection, and semantic segmentation. Of particular importance, we believe that it is time to shift focus from spatial features to receptive-field spatial features for current spatial attention mechanisms. By doing so, we can further improve network performance and achieve even better results. The code and pre-trained models for the relevant tasks can be found at https://github.com/Liuchen1997/RFAConv.Comment: 14 pages, 5 figure