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Spectral Clustering (SC) is an important method in areas such as data mining, image processing, computer science and so on. It attracts more and more attention owing to its effectiveness in unsupervised learning. However, SC has poor performance in the high-dimensional data. Traditional SC methods conduct the spectral embedding of the affinity matrix among data at the first beginning, and then obtain clustering results by the K -means clustering. The also have drawbacks int two processing steps: the clustering results are sensitive to the affinity matrix which may be inaccurate and the post-processing K -means may also be limited by its initialization problem. In the paper, a new approach which joints spectral embedding and clustering with structured graph optimization (called JSEGO) is proposed. In the new model, the low-dimensional representation of data can first be obtained by the spectral embedding method, which can handle with the high-dimensional data better. Then, the optimization similarity matrix would be obtained with such the embedded data. Furthermore, the learning structure graph gives feedback to the similarity matrix to generate better spectral embedded data. As a result, better similarity matrix and clustering result can be obtained by the iterations simultaneously, which are often conducted in two separate steps in the spectral clustering. As a result, the drawbacks introduced by the two processing introduces can be solved. At last, we use an alternative optimization method in the new model and conduct the theoretical analysis by comparing this proposed method with K -means clustering. Experiments based on synthetic data and actual benchmark data prove the advantage of this new approach. [ABSTRACT FROM AUTHOR]

The seven papers included in this special issue represent a selection of extended contributions presented at the 16th International Conference on Soft Computing Models in Industrial and Environmental Applications, SOCO 2021, held in Bilbao, Spain, September 22nd-24th, 2021, and organized by the BISITE group and the University of Deusto. The SOCO 2021 international conference represents a collection or set of computational techniques in machine learning, computer science and some engineering disciplines that investigate, simulate, and analyse very complex issues and phenomena. This special issue is aimed at practitioners, researchers, and postgraduate students who are engaged in developing and applying advanced intelligent systems principles to solve real-world problems in the mentioned fields. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problem (COP) is an NP-hard problem for which finding an optimal solution is difficult, especially as the problem size increases. The Traveling Salesman Problem (TSP), one of the COPs that can be formulated over a graph, is a well-researched area in operations research and computer science. Deep Reinforcement Learning (DRL) is now regarded as a promising approach for solving TSP and other NP hard problems. In this paper, we propose a novel Gated Deep Graph Attention Network (G-DGANet) which builds upon the existing Graph Neural Network (GNN) to solve TSP. The proposed G-DGANet uses gating mechanism between subsequent layers of the network to extract representations of nodes deeper in the network without loss in performance. G-DGANet also designs a novel aggregator to construct global graph embeddings from different embedding preferences. In addition, to effectively learn underlying structure of a graph, G-DGANet integrates node and edge information of the graph while updating node representations in the message passing mechanism. We used proximal policy optimization (PPO) to train G-DGANet on randomly generated instances. We conducted an experiment on randomly generated instances and on real-world road network data generated from digital maps to verify the performance of G-DGANet. The findings from experiments demonstrate that G-DGANet outperforms most traditional heuristics and existing DRL approaches, with high generalization abilities from random instance training to random instance testing and real-world road network instance testing. [ABSTRACT FROM AUTHOR]

The problem of subspace clustering which refers to segmenting a collection of data samples approximately drawn from a union of linear subspaces is considered in this paper. Among existing subspace clustering algorithms, low rank representation (LRR) based subspace clustering is a very powerful method and has demonstrated that its performance is good. Latent low rank representation (LLRR) subspace clustering algorithm is an improvement of the original LRR algorithm when the observed data samples are insufficient. The clustering accuracy of LLRR is higher than that of LRR. Recently, Frobenius norm minimization based LRR algorithm has been proposed and its clustering accuracy is higher than that of LRR demonstrating the effectiveness of Frobenius norm as another convex surrogate of the rank function. Combining LLRR and Frobenius norm, a new low rank representation subspace clustering algorithm is proposed in this paper. The nuclear norm in the LLRR algorithm is replaced by the Frobenius norm. The resulting optimization problem is solved via alternating direction method of multipliers (ADMM). Experimental results show that compared with LRR, LLRR and several other state-of-the-art subspace clustering algorithms, the proposed algorithm can get higher clustering accuracy. Compared with LLRR, the running time of the proposed algorithm is reduced significantly. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on how to construct concept lattice effectively and efficiently based on improved variable precision rough set. On the basis of preprocessing formal concept, one algorithm that can determine the value range of variable precision parameter β according to the approximate classification quality is proposed. An improved β -upper and lower distribution attribute reduction algorithm is also proposed based on the improved variable precision rough set, the algorithm can be used for attribute reduction on the original data of the concept lattice, and to eliminate the redundant knowledge or noises of the formal context. For the reduced formal context, the paper combines the concept construction algorithm with an improved rule acquisition algorithm seamlessly, and proposes a novel approach of concept lattice construction based on improved variable precision rough set. Finally, a concept lattice generation prototype system is developed, this paper also performs comprehensive experiments, and the effectiveness of the improved algorithm is proved through the experimental results. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for identifying data samples that are likely to be mislabeled in a c -class classification problem (dataset). The methodology relies on an assumption that the generalization error of a model learned from the data decreases if a label of some mislabeled sample is changed to its correct class. A general classification model used in the paper is OP-ELM; it also provides a fast way to estimate the generalization error by PRESS Leave-One-Out. It is tested on two toy datasets, as well as on real life datasets for one of which expert knowledge about the identified potential mislabels has been sought. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes food image classification methods exploiting both local appearance and global structural information of food objects. The contribution of the paper is threefold. First, non-redundant local binary pattern (NRLBP) is used to describe the local appearance information of food objects. Second, the structural information of food objects is represented by the spatial relationship between interest points and encoded using a shape context descriptor formed from those interest points. Third, we propose two methods of integrating appearance and structural information for the description and classification of food images. We evaluated the proposed methods on two datasets. Experimental results verified that the combination of local appearance and structural features can improve classification performance. [Copyright &y& Elsevier]

Abstract: Similarity measure plays an important role in many image processing fields. This paper introduces the medium mathematic systems, and establishes a novel image medium similarity measure between two pixels and that of between two image sets based on the measure of medium truth degree. Moreover, an image edge detection algorithm, an image matching algorithm and an image medium fidelity measure method governed by the medium similarity measure are discussed in this paper. Experimental results show that the proposed similarity measure is effective. [Copyright &y& Elsevier]