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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 eight papers included in this special issue represent a selection of extended contributions presented at the 17th International Conference on Soft Computing Models in Industrial and Environmental Applications, SOCO 2022 held in Salamanca, Spain, September 6th-8th, 2022, and organized by the BISITE group at University of Salamanca. SOCO 2022 international conference represents a collection or set of computational techniques in machine learning, computer science and some engineering disciplines which 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 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]

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]

The seven papers included in this special issue represent a selection of extended contributions presented at the 15th International Conference on Soft Computing Models in Industrial and Environmental Applications, SOCO 2020, held in Burgos, Spain, September 2020, and organized by University of Burgos and BISITE and GICAP Research Groups. SOCO 2020 international conference represents a collection or set of computational techniques in machine learning, computer science and some engineering disciplines which 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 solving real-world problems on the mentioned fields. [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]

Multiple object tracking is a key problem for many computer vision applications such as video surveillance, advanced driver assistance or animation. Most of existing tracking-by-detection methods are mainly based on object appearances and motions. However, the contextual information around the target has not been fully exploited. In this paper, we pay more attention to the contextual information and propose an Exchanging Object Context (EOC) model, which takes full advantage of the context information. Specifically, we implement an efficient and accurate online multiple object tracking algorithm with a novel affinity measure to associate detections. This measure calculates the similarity between targets and detections with the background smoothness after exchanging the contexts between detections and targets, using a novel color histogram descriptor. We refine the bounding boxes by measuring the context changes. Extensive experimental results on two public benchmarks demonstrate the effectiveness of the proposed tracking method with comparisons to several state-of-the-art trackers. [ABSTRACT FROM AUTHOR]

Neighborhood models ( NBM s) are the methods widely used for collaborative filtering in recommender systems. Given a target user and a target item, NBM s find k most similar users or items (i.e., k -nearest neighbors) and make a prediction of a target user on an item based on the rating patterns of those neighbors on the item. In NBM s, however, we have a difficulty in satisfying both the performance and accuracy together. In order to pursue an accurate recommendation, NBM s may find the k -nearest neighbors at every recommendation request to exploit the latest ratings, which requires a huge amount of computation time. Alternatively, NBM s may search for the k -nearest neighbors offline, which consequently results in inaccurate recommendation as time goes by, or even may not able to deal with new users or new items, because they cannot exploit the latest ratings generated after the k -nearest neighbors are determined. In this paper, we propose a novel approach that finds the k -nearest neighbors efficiently by identifying only those users and items necessary in computing the similarity. The proposed approach enables NBM s not to require any offline similarity computations but to exploit the latest ratings, thereby resolving speed-accuracy tradeoff successfully. We demonstrate the effectiveness of the proposed approach through extensive experiments. [ABSTRACT FROM AUTHOR]

Learning rich representations efficiently plays an important role in the multi-modal recognition task, which is crucial to achieving high generalization performance. To address this problem, in this paper, we propose an effective Multi-Modal Local Receptive Field Extreme Learning Machine (MM-LRF-ELM) structure, while maintaining ELM’s advantages of training efficiency. In this structure, LRF-ELM is first conducted for feature extraction for each modality separately. And then, the shared layer is developed by combining these features from each modality. Finally, the Extreme Learning Machine (ELM) is used as supervised feature classifier for the final decision. Experimental validation on Washington RGB-D Object Dataset illustrates that the proposed multiple modality fusion method achieves better recognition performance. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient and effective active online sequential learning approach, named as Less Annotated Active Learning Extreme Learning Machine (LAAL-ELM). It leverages the predictions’ confidence of the new arriving data to actively select both query-annotated samples and confidence-weighted predict-annotated ones to update the classifier, which contributes to less actively query annotation, and applies WOS-ELM, a discriminant model, to significantly reduce the computation complexity for doing online updating in one step. The proposed approach firstly gives a principle to evaluate confidence of the prediction in WOS-ELM; then determines what and how to update the model with new arriving data in the online phase: the uncertain instances are annotated by query their classes, almost-certain ones are weighted on its prediction’s confidence and the certain ones are discarded directly for reducing over-fitting; at last, the weighted and query-annotated samples are used to update the classifier. The proposed approach is evaluated on five real-world benchmark classification issues. And the experimental results demonstrate that the proposed LAAL-ELM can effectively reduce the number of queried samples while maintaining high level of classification performance. [ABSTRACT FROM AUTHOR]

This paper presents a novel unsupervised multi-source domain adaptation approach, named as coupled local–global adaptation (CLGA). At the global level, in order to maximize the adaptation ability, CLGA regards multiple domains as a unity, and jointly mitigates the gaps of both marginal and conditional distributions between source and target dataset. At the local level, with the intention of maximizing the discriminative ability, CLGA investigates the relationship among distinctive domains, and exploits both class and domain manifold structures embedded in data samples. We formulate both local and global adaptation in a concise optimization problem, and further derive an analytic solution for the objective function. Extensive evaluations verify that CLGA performs better than several existing methods not only in multi-source adaptation tasks but also in single source scenarios. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) has been one of the great successes of applied mathematics in the last decade. This paper proposes a new method, combining the advantage of the Compressive Sampling Matching Pursuit (CoSaMP) algorithm and the Quasi–Newton Iteration Projection (QNIP) algorithm, for the recovery of sparse signal from underdetermined linear systems. To get the new algorithm, Quasi–Newton Projection Pursuit (QNPP), the least-squares technique in CoSaMP is used to accelerate convergence speed and QNIP is modified slightly. The convergence rate of QNPP is studied, under a certain condition on the restricted isometry constant of the measurement matrix, which is smaller than that of QNIP. The fast version of QNPP is also proposed which uses the Richardson’s iteration to reduce computation time. The numerical results show that the proposed algorithms have higher recovery rate and faster convergence speed than existing techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a special class of recurrent neural network, termed Zhang neural network (ZNN), is investigated for the online solution of the time-varying matrix pseudoinverse. Meanwhile, a novel activation function, named Li activation function, is employed. Then, based on two basic Zhang functions (ZFs) and the intrinsically nonlinear method of ZNN design, two finite-time convergent ZNN models (termed ZNN-1 model and ZNN-2 model) are first proposed and investigated for time-varying matrix pseudoinversion. Such two ZNN models can be accelerated to finite-time convergence to the time-varying theoretical pseudoinverse. The upper bound of the convergence time is also derived analytically via Lyapunov theory. By exploiting the other three simplified ZFs and the extended nonlinearization method, three simplified finite-time convergent ZNN models (termed ZNN-3 model, ZNN-4 model and ZNN-5 model) are sequentially proposed. In addition, the link between the ZNN models and the Getz–Marsden (G–M) dynamic system is discovered and presented in this paper. Computer-simulation results further substantiate the theoretical analysis and demonstrate the effectiveness of ZNN models based on different ZFs for the time-varying matrix pseudoinverse. [Copyright &y& Elsevier]

The Box–Cox transformation [1,2] (Box and Cox, 1964; Sakia, 1992) has been regarded as a parametric pre-processing technique aimed at making the distribution of a set of points approximately Gaussian. Since normality represents an assumption underlying many statistical data analysis tools, such technique has been widely applied in different fields of Computer Science. In this paper we will provide evidence that this technique can be useful also in the case of Pattern Classification, where Gaussianity of datasets is not so critical. By letting the Box–Cox transform work in operational ranges which do not necessarily correspond to an increase in Gaussianity, we will show that class separability can be improved: this is likely due to the non linear nature of the Box–Cox transformation, which deforms the space in a nonuniform way. We will also provide some suggestions on criteria that can be used to automatically estimate the best parameter of the Box–Cox transformation in the Pattern Classification context. [ABSTRACT FROM AUTHOR]

Online Social Networks (OSNs) have been used as the means for a variety of applications. For example, social networking platform has been used in employment system, e-Commerce and CRM system to improve the quality of recommendations with the assistance of social networks. In these applications, social influence acts as a significant role, affecting people's decision-making. However, the existing social influence evaluation methods do not fully consider the social contexts, i.e., the social relationships and the social trust between participants, and the preferences of participants, which have significant impact on social influence evaluation in OSNs. Thus, these existing methods cannot deliver accurate social influence evaluation results. In our paper, we propose a Trust-Oriented Social Influence evaluation method, called TOSI , with taking the social contexts into account. We conduct experiments onto two real social network datasets, i.e., Epinions and DBLP . The experimental results illustrate that our TOSI method greatly outperforms the state-of-the-art method SoCap in terms of effectiveness, efficiency and robustness. [ABSTRACT FROM AUTHOR]

Community detection is an important task for uncovering underlying structures and analyzing group behavior in complex networks. A fuzzy community detection method is proposed in this paper to detect fuzzy community structures without any prior knowledge. Compared with previous studies, we introduce a structural similarity to measure fuzzy relation between vertices based on local interactions between neighboring vertices. In our method, we take the fuzzy similarity between vertices and fuzzy transitivity of the similarity in network topology into consideration. Moreover, multiresolution community structures can be detected by varying the fuzzy threshold. Experimental results and comparisons with some state-of-the-art methods are presented on a variety of benchmark graphs. It shows that the method is efficient in detecting communities on both real-world and synthetic networks. [ABSTRACT FROM AUTHOR]

This paper studies the self-triggered control consensus problem of general linear multi-agent systems(MASs). A novel self-triggered control strategy based on output feedback is proposed for centralized and distributed cases, respectively. In consideration of the states of agents that are not available, a state observer is adopted. A dynamic observer-based control law is employed to improve the transient response. Under this triggering strategy, both the estimated states of MASs and the states of controller are updated at triggering time. The next triggering time is predetermined at the last triggering instant. Moreover, the asymptotic consensus of MASs can be guaranteed. Finally, the effectiveness of the proposed control strategy is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

A slap fingerprint based verification system generally is highly secure. But it cannot handle the problems of temporal deformation and pose variation. In this paper, a template update algorithm has been proposed to ensure better performance of the system. During verification, each single fingerprint is matched and matching scores of all fingerprints are fused using an adaptive score level fusion. The performance of the proposed system has been evaluated on a challenging database containing 1800 slap-images acquired from 150 subjects. Experimental results show that the accuracy is increased by more than 3.5%. [ABSTRACT FROM AUTHOR]

The presence of noise in real data sets can harm the predictive performance of machine learning algorithms. There are several noise filtering techniques whose goal is to improve the quality of the data in classification tasks. These techniques usually scan the data for noise identification in a preprocessing step. Nonetheless, this is a non-trivial task and some noisy data can remain unidentified, while safe data can also be removed. The bias of each filtering technique influences its performance on a particular data set. Therefore, there is no single technique that can be considered the best for all domains or data distribution and choosing a particular filter is not straightforward. Meta-learning has been largely used in the last years to support the recommendation of the most suitable machine learning algorithm(s) for a new data set. This paper presents a meta-learning recommendation system able to predict the expected performance of noise filters in noisy data identification tasks. For such, a meta-base is created, containing meta-features extracted from several corrupted data sets along with the performance of some noise filters when applied to these data sets. Next, regression models are induced from this meta-base to predict the expected performance of the investigated filters in the identification of noisy data. The experimental results show that meta-learning can provide a good recommendation of the most promising filters to be applied to new classification data sets. [ABSTRACT FROM AUTHOR]

Noise is common in any real-world data set and may adversely affect classifiers built under the effect of such type of disturbance. Some of these classifiers are widely recognized for their good performance when dealing with imperfect data. However, the noise robustness of the classifiers is an important issue in noisy environments and it must be carefully studied. Both performance and robustness are two independent concepts that are usually considered separately, but the conclusions reached with one of these metrics do not necessarily imply the same conclusions with the other. Therefore, involving both concepts seems to be crucial in order determine the expected behavior of the classifiers against noise. Existing measures fail to properly integrate these two concepts, and they are also not well suited to compare different techniques over the same data. This paper proposes a new measure to establish the expected behavior of a classifier with noisy data trying to minimize the problems of considering performance and robustness individually: the Equalized Loss of Accuracy (ELA). The advantages of ELA against other robustness metrics are studied and all of them are also compared. Both the analysis of the distinct measures and the empirical results show that ELA is able to overcome the aforementioned problems that the rest of the robustness metrics may produce, having a better behavior when comparing different classifiers over the same data set. [ABSTRACT FROM AUTHOR]

In this paper we introduce a simple and efficient extension of the Extreme Learning Machine (ELM) network (Huang et al., 2006 [19] ), which is very robust to label noise, a type of outlier occurring in classification tasks. Such outliers usually result from mistakes during labeling of the data points (e.g. misjudgment of a specialist) or from typing errors during creation of data files (e.g. by striking an incorrect key on a keyboard). The proposed variant of the ELM, henceforth named Robust ELM (RELM), is designed using M -estimators to compute the output weights instead of the standard ordinary least squares (OLS) method. We evaluate the performance of the RELM using batch and recursive learning rules, and also introduce a model selection strategy based on Particle Swarm Optimization (PSO) to find an optimal architecture for datasets contaminated with non-Gaussian noise and outliers. By means of comprehensive computer simulations using synthetic and real-world datasets, we show that the proposed Robust ELM classifiers consistently outperforms the original version. [ABSTRACT FROM AUTHOR]

In this paper, we show how to learn a hyperplane regressor by minimizing a tight or Θ bound on its VC dimension. While minimizing the VC dimension with respect to the defining variables is an ill posed and intractable problem, we propose a smooth, continuous, and differentiable function for a tight bound. Minimizing a tight bound yields the Minimal Complexity Machine (MCM) Regressor, and involves solving a simple linear programming problem. Experimental results show that on a number of benchmark datasets, the proposed approach yields regressors with error rates much lower than those obtained with conventional SVM regresssors, while often using fewer support vectors. On some benchmark datasets, the number of support vectors is less than one-tenth the number used by SVMs, indicating that the MCM does indeed learn simpler representations. [ABSTRACT FROM AUTHOR]

Anchorgraph based learning methods have met with success in modeling the large data for scalable semi-supervised learning. However, like most graph based learning algorithms, they are usually built with a randomly selected labeled set classified in advance. Although many pool-based active learning methods have been proposed, they often require a relatively large computational and storage consumption, which tends to impose extra burden on the learning system. Thus in this paper, we propose a novel active learning method named anchor-based transductive experimental design (ATED). By fully utilizing the representing power of anchors, the improved method efficiently enhances the performance of the original anchorgraph based learning while introduces much less extra cost on computation and storage. Extensive experimental results on real-world datasets have validated our approach in terms of classifying accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

By introducing an identity occlusion dictionary to encode the occluded part on the source image, sparse representation based classification has shown good performance on ear recognition under partial occlusion. However, large number of atoms of the conventional occlusion dictionary brings expensive computational load to the SRC model solving. In this paper, we propose a non-negative dictionary based sparse representation and classification scheme for ear recognition. The non-negative dictionary includes the Gabor features dictionary extracted from the ear images, and non-negative occlusion dictionary learned from the identity occlusion dictionary. A test sample with occlusion can be sparsely represented over the Gabor feature dictionary and the occlusion dictionary. The sparse coding coefficients are noted with non-negativity and much more sparsity, and the non-negative dictionary has shown increasing discrimination ability. Experimental results on the USTB ear database show that the proposed method performs better than existing ear recognition methods under partial occlusion based on SRC. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an ear recognition technique which makes use of 3D along with co-registered 2D ear images. It presents a two-step matching technique to compare two 3D ears. In the first step, it computes salient 3D data points from 3D ear images with the help of local 2D feature points of co-registered 2D ear images. Subsequently, it uses these salient 3D points to coarsely align 3D ear images. In the second step, it performs final matching of coarsely aligned 3D ear images by using a Generalized Procrustes Analysis (GPA) and Iterative Closest Point (ICP) based matching technique (GPA-ICP). The proposed technique has been tested on 1780 images of 404 subjects (two or more images per subject) of University of Notre Dame public database-Collection J2 (UND-J2) which consists of co-registered 2D and 3D ear images with scale and pose variations. It has achieved a verification accuracy of 98.30% with an equal error rate of 1.8%. [Copyright &y& Elsevier]

Abstract: In this paper, an efficient feature extraction method, named local structure preserving discriminant analysis (LSPDA), is presented. LSPDA constructs the local scatter and the between-class scatter to characterize the sub- and multi-manifold information respectively. More specifically, the local structure is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information based on a parameter-free neighborhood decision rule, and the between-class structure is constructed according to the importance degrees of the not-same-class points measured by a strictly monotonically decreasing function. After the local scatter and the between-class scatter have been characterized, the novel feature extraction criterion is derived via maximizing the difference between the between-class scatter and the local scatter. Experimental results on the Wine dataset, AR, FERET, CMU PIE, ORL and LFW face databases show the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In the theory of differential geometry, surface normal, as a first order surface differential quantity, determines the orientation of a surface at each point and contains informative local surface shape information. To fully exploit this kind of information for 3D face recognition (FR), this paper proposes a novel highly discriminative facial shape descriptor, namely multi-scale and multi-component local normal patterns (MSMC-LNP). Given a normalized facial range image, three components of normal vectors are first estimated, leading to three normal component images. Then, each normal component image is encoded locally to local normal patterns (LNP) on different scales. To utilize spatial information of facial shape, each normal component image is divided into several patches, and their LNP histograms are computed and concatenated according to the facial configuration. Finally, each original facial surface is represented by a set of LNP histograms including both global and local cues. Moreover, to make the proposed solution robust to the variations of facial expressions, we propose to learn the weight of each local patch on a given encoding scale and normal component image. Based on the learned weights and the weighted LNP histograms, we formulate a weighted sparse representation-based classifier (W-SRC). In contrast to the overwhelming majority of 3D FR approaches which were only benchmarked on the FRGC v2.0 database, we carried out extensive experiments on the FRGC v2.0, Bosphorus, BU-3DFE and 3D-TEC databases, thus including 3D face data captured in different scenarios through various sensors and depicting in particular different challenges with respect to facial expressions. The experimental results show that the proposed approach consistently achieves competitive rank-one recognition rates on these databases despite their heterogeneous nature, and thereby demonstrates its effectiveness and its generalizability. [Copyright &y& Elsevier]