Sparse Regularization Research Articles

Video Summarization using Attention Mechanisms and CNN

This Video summarization is a vital task in multimedia analysis, especially given the vast volume of video data in the digital age. Although deep learning methods have been extensively studied for this purpose, they often face challenges in efficiently processing long-duration videos. This paper tackles the issue of unsupervised video summarization by introducing a novel approach that selects a sparse subset of video frames to optimally represent the original video. The core concept involves training a deep summarizer network within a generative adversarial framework, which includes an autoencoder LSTM network as the summarizer and another LSTM network as the discriminator. The summarizer LSTM is designed to select key video frames and reconstruct the input video from these selected frames. Concurrently, the discriminator LSTM's role is to differentiate between the original video and its reconstruction. Through adversarial training between the summarizer and discriminator, combined with sparsity regularization, the network learns to produce optimal video summaries without requiring labeled data. Evaluations on several benchmark datasets indicate that this method delivers competitive performance compared to fully supervised state-of-the-art techniques, highlighting its effectiveness in unsupervised video summarization. Key Words: Event summarization, Critical information in videos, Surveillance systems ,Video analysis, Multimedia analysis, Deep learning, Unsupervised learning, Autoencoder LSTM, Long short-term memory network (LSTM)

Structured learning in time-dependent Cox models.

Cox models with time-dependent coefficients and covariates are widely used in survival analysis. In high-dimensional settings, sparse regularization techniques are employed for variable selection, but existing methods for time-dependent Cox models lack flexibility in enforcing specific sparsity patterns (ie, covariate structures). We propose a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules. Our method can adapt to arbitrary grouping structures, including interaction selection, temporal, spatial, tree, and directed acyclic graph structures. It achieves accurate estimation with low false alarm rates. We develop the sox package, implementing a network flow algorithm for efficiently solving models with complex covariate structures. sox offers a user-friendly interface for specifying grouping structures and delivers fast computation. Through examples, including a case study on identifying predictors of time to all-cause death in atrial fibrillation patients, we demonstrate the practical application of our method with specific selection rules.

Sparse deep encoded features with enhanced sinogramic red deer optimization for fault inspection in wafer maps

AbstractDue to the complexity and dynamics of the semiconductor manufacturing processes, wafer bin maps (WBM) present various defect patterns caused by various process faults. The defect type detection on wafer maps provides information about the process and equipment in which the defect occurred. Recently, automatic inspection has played a vital role in meeting the high-throughput demand, especially with deep convolutional neural networks (DCNN) which shows promising efficiency. At the same time, the need for a large amount of labeled and balanced datasets limits the performance of such approaches. In addition, complex DCNN in recognition tasks can provide redundant features that cause overfitting and reduce interpretability. In this paper, a new hybrid deep model for wafer map fault detection to get over these challenges is proposed. Firstly, a new convolutional autoencoder (CAE) is employed as a synthetization model to fix the high imbalance problem of the dataset. Secondly, for efficient dimensionality reduction, an embedding procedure is applied to the synthesized maps to get sparse encoded wafer maps by reinforcing a sparsity regularization in an encoder-decoder network to form a sparsity-boosted autoencoder (SBAE). The sparse embedding of wafer maps guarantees more discriminative features with 50% reduction in spatial size compared to the original wafer maps. Then, the 2D encoded sparse maps are converted to 1D sinograms to be fed later into another aggressive feature reduction stage using a new modified red deer algorithm with a new tinkering strategy. The resultant feature pool is reduced to ~ 25 1D feature bases, i.e., ~ 1.5% of the initial size of the 2D wafer maps. Finally, for the prediction stage, a simple 1DCNN model is introduced. The proposed inspection model is tested via different experiments on real-world wafer map dataset (WM-811K). Compared to state-of-the-art techniques, the proposed model outperforms their performance even with small-sized 1D feature pool. The average testing accuracy are 98.77% and 98.8% for 9 and 8 types of faults, respectively.

[formula omitted] sparsity regularization for nonlinear ill-posed problems

In this paper, the α‖⋅‖ℓ1−β‖⋅‖ℓ2 sparsity regularization with parameters α≥β≥0 is studied for nonlinear ill-posed inverse problems. The well-posedness of the regularization is investigated. Compared to the case where α>β≥0, the results for the case α=β>0 are weaker due to the lack of coercivity and Radon-Riesz property of the regularization term. Under certain conditions on the nonlinearity of F, sparsity is shown for every minimizer of the α‖⋅‖ℓ1−β‖⋅‖ℓ2 regularized inverse problem. Moreover, for the case α>β≥0, convergence rates O(δ12) and O(δ) are proved for the regularized solution toward a sparse exact solution, under different yet commonly adopted conditions on the nonlinearity of F. The iterative soft thresholding algorithm is shown to be useful to solve the α‖⋅‖ℓ1−β‖⋅‖ℓ2 regularized problem for nonlinear ill-posed equations. Numerical results illustrate the efficiency of the proposed method.

EPK-CLIP: External and Priori Knowledge CLIP for action recognition

Contrastive Language-Image Pretraining (CLIP) models have achieved significant success and have markedly improved the performance of various downstream tasks, including action recognition. However, how to effectively introduce knowledge into the field of action recognition remains an open question. In this work, an External and Priori Knowledge CLIP (EPK-CLIP) is proposed to introduce external knowledge into the model. To capture external knowledge, an external knowledge embedding module is proposed, which can generate and utilize human-object interaction relations as external knowledge, enabling the model to learn better features. Furthermore, the sparse regularization is introduced in the loss function, endowing the model with the ability to exploit the sparse priori knowledge inherent in the classification task. Finally, multiple inference module is proposed to obtain classification results from both direct and indirect perspectives. Specifically, the final classification result is obtained by fusing the outputs of different reasoning modules. Moreover, four external knowledge datasets: Kinetics-400-VC, Jester-VC, HMDB-51-VC, and UCF-101-VC are built and released for public usage, which is a multimodal extension of corresponding action datasets respectively. Under fully-supervised settings, our model achieves the top-1 accuracy of 84.3%, 97.1%, 82.9%, and 98.2% on Kinetics-400, Jester, HMDB-51, and UCF-101, respectively. In zero-shot experiments, our model also achieves state-of-the-art results, with top-1 accuracy of 51.6% and 77.7% on HMDB-51 and UCF-101, respectively. All related datasets and code can be found at https://github.com/geek12138/EPK-CLIP.

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

Robust sparse representation based on fitting error decomposition

Sparse representation (SR) of a signal aims at finding the minimum number of atoms for its representation. In several practical scenarios, the signal is vulnerable to outliers and thus robustness is required for SR based algorithms. However, most existing robust schemes are designed on the assumption that the anomalies are independently distributed, which may not perform well encountering complex interferences, especially the correlated ones. To deal with this drawback, a robust SR model is proposed, where both independent and correlated outliers are considered. Specifically, the fitting error is decomposed as the combination of a low-rank component and a sparse part, corresponding to the correlated gross error and independent outlier, respectively. Then, the group sparsity of the representation coefficient is utilized. Moreover, ℓ0-norm and ℓ2,0-norm are adopted as the sparsity regularization for the sparse outlier and representation coefficients, respectively. The solutions to ℓ0/ℓ2,0-norm minimization are generated by the hard-thresholding strategy, where the decision threshold is adaptively determined using median absolute deviation operator. As for the low-rank regularization, due to the NP-hardness of rank minimization, we employ matrix logarithmic norm as the rank surrogate to lessen the approximation gap. Finally, we apply the proposed model to face recognition task, and the excellent performance demonstrates its effectiveness.

An efficient training-from-scratch framework with BN-based structural compressor

Channel pruning is an effective way of compressing convolutional neural networks (CNNs) under constrained resources. The current pruning methods follow a progressive pretrain-prune-finetune pipeline, which is inefficient and computationally expensive. In this paper, we bypass the pretrain-prune-finetune pipeline and propose a novel and efficient model training framework based on online channel pruning, which automatically produces a compact well-performed sub-network in one training-from-scratch pass under a given budget condition. Specifically, we introduce a novel BN-based indicator and a sparsity regularization strategy in the early training stage to iteratively and greedily shrink the model layers, which encourages a high-quality architecture with low channel redundancy. To ensure training stability and promote the generalization ability of the resultant pruned network, we also skillfully incorporate a simple self-distillation framework into our training and pruning pipeline. Extensive experiments indicate that our method can effectively achieve competitive performance on the image classification task compared with the state-of-the-arts.

NOODLE: Joint Cross-View Discrepancy Discovery and High-Order Correlation Detection for Multi-View Subspace Clustering

Benefiting from the effective exploration of the valuable topological pair-wise relationship of data points across multiple views, multi-view subspace clustering (MVSC) has received increasing attention in recent years. However, we observe that existing MVSC approaches still suffer from two limitations that need to be further improved to enhance the clustering effectiveness. Firstly, previous MVSC approaches mainly prioritize extracting multi-view consistency, often neglecting the cross-view discrepancy that may arise from noise, outliers, and view-inherent properties. Secondly, existing techniques are constrained by their reliance on pair-wise sample correlation and pair-wise view correlation, failing to capture the high-order correlations that are enclosed within multiple views. To address these issues, we propose a novel MVSC framework via joi N t cr O ss-view discrepancy disc O very an D high-order corre L ation d E tection ( NOODLE ), seeking an informative target subspace representation compatible across multiple features to facilitate the downstream clustering task. Specifically, we first exploit the self-representation mechanism to learn multiple view-specific affinity matrices, which are further decomposed into cohesive factors and incongruous factors to fit the multi-view consistency and discrepancy, respectively. Additionally, an explicit cross-view sparse regularization is applied to incoherent parts, ensuring the consistency and discrepancy to be precisely separated from the initial subspace representations. Meanwhile, the multiple cohesive parts are stacked into a three-dimensional tensor associated with a tensor-Singular Value Decomposition (t-SVD) based weighted tensor nuclear norm constraint, enabling effective detection of the high-order correlations implicit in multi-view data. Our proposed method outperforms state-of-the-art methods for multi-view clustering on six benchmark datasets, demonstrating its effectiveness.

Towards robust and sparse linear discriminant analysis for image classification

Linear discriminant analysis (LDA) is a popular dimensionality reduction technique that has been widely used in pattern recognition. However, there exist a large number of redundant features and corrupted noise in real-world applications, which makes the performance of existing LDA methods degrade and thus leads to a decrease in classification accuracy. To address the above issues, we propose a novel robust and sparse LDA formulation dubbed RSLDA+. The key idea is introducing the mixed sparse regularization, i.e., ℓ0-norm plus ℓ2,0-norm, for feature representation and enforce ℓ0-norm for noise reduction. Furthermore, an optimization algorithm based on the alternating direction method of multipliers (ADMM) is developed in combination with hard thresholding operators. Extensive experiments on six common image datasets verify that the proposed RSLDA+ outperforms state-of-the-art LDA variants in classification accuracy. In addition, the ablation, robustness, convergence, stability, and sparsity are analyzed in detail. The results suggest that the proposed RSLDA+ provides an effective and robust method for image classification.

High-resolution acoustic imaging method based on equivalent source method and reweighted l1 minimization

Sparse regularization has been successfully applied to equivalent source method (ESM) in order to improve the acoustic imaging resolution. However, the application is not always feasible, especially at low frequencies. To overcome the problem, this paper proposes a high-resolution acoustic imaging method. In this method, reweighted l1 minimization is introduced to ESM to deal with the ill-posed inverse problems. Then the obtained equivalent source strengths are used to locate the sound sources. Compared to the sparse regularization-based ESM, the proposed method can provide a low side lobe and higher spatial resolution of acoustic imaging. Meanwhile, by arranging equivalent sources in three-dimensional space, the proposed method can also realize the acoustic imaging in three-dimensional sound field with high resolution. The results of the simulation and experiment demonstrate the validations.

Bearing Fault Diagnosis via Stepwise Sparse Regularization with an Adaptive Sparse Dictionary.

Vibration monitoring is one of the most effective approaches for bearing fault diagnosis. Within this category of techniques, sparsity constraint-based regularization has received considerable attention for its capability to accurately extract repetitive transients from noisy vibration signals. The optimal solution of a sparse regularization problem is determined by the regularization term and the data fitting term in the cost function according to their weights, so a tradeoff between sparsity and data fidelity has to be made inevitably, which restricts conventional regularization methods from maintaining strong sparsity-promoting capability and high fitting accuracy at the same time. To address the limitation, a stepwise sparse regularization (SSR) method with an adaptive sparse dictionary is proposed. In this method, the bearing fault diagnosis is modeled as a multi-parameter optimization problem, including time indexes of the sparse dictionary and sparse coefficients. Firstly, sparsity-enhanced optimization is conducted by amplifying the regularization parameter, making the time indexes and the number of atoms adaptively converge to the moments when impulses occur and the number of impulses, respectively. Then, fidelity-enhanced optimization is carried out by removing the regularization term, thereby obtaining the high-precision reconstruction amplitudes. Simulations and experiments verify that the reconstruction accuracy of the SSR method outperforms other sparse regularization methods under most noise conditions, and thus the proposed method can provide more accurate results for bearing fault diagnosis.

Self-paced regularized adaptive multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) is an efficient approach for dimensional reduction of heterogeneous data. However, existing MUFS approaches mostly assign the samples the same weight, thus the diversity of samples is not utilized efficiently. Additionally, due to the presence of various regularizations, the resulting MUFS problems are often non-convex, making it difficult to find the optimal solutions. To address this issue, a novel MUFS method named Self-paced Regularized Adaptive Multi-view Unsupervised Feature Selection (SPAMUFS) is proposed. Specifically, the proposed approach firstly trains the MUFS model with simple samples, and gradually learns complex samples by using self-paced regularizer. l2,p-norm (0<p≤1) is employed to measure the learning error and as the sparse regularization to accommodate various sparsity requirements across different datasets. Moreover, hypergraph Laplacian matrices are constructed for each view to better preserve the local manifold structure and encode high-order relationships within the data space. They are adaptively assigned weights to learn the underlying correlated and diverse information among different views. An iterative optimization algorithm is proposed to solve SPAMUFS and the convergence and computational complexity are also analyzed. The effectiveness of SPAMUFS is substantiated by comparing with eight state-of-the-art algorithms on nine public multi-view datasets.

Towards multi-scene learning: A novel cross-domain adaptation model based on sparse filter for traction motor bearing fault diagnosis in high-speed EMU

Fault diagnosis of traction motor bearing is of great significance to improve the reliability and safety of high-speed electric multiple units (EMU). While the fault diagnosis method based on cross-domain adaptation has been successful in scenarios involving speed or load fluctuations, existing methods ignore the independence and diversity of features, resulting in unsatisfactory diagnostic results under multi-scene learning, thereby reducing the generalization ability. Moreover, the development of complex models is time-consuming, and their computational efficiency is low. To address these issues, this study proposes a novel cross-domain adaptation model based on sparse filtering (SFCDA), which consists of only two fully connected (FC) layers. Firstly, pre-training is conducted to utilize the soft reconstruction penalties to constrain the weights of sparse filtering and improve the independence of features. The weights of unsupervised training are used to initialize the parameters of the first FC layer of the SFCDA model. Secondly, a multiple sparse regularization (MSR) algorithm is proposed and used to constrain the SFCDA. Then, fine-tuning is conducted, in which the structural alignment function is used to measure the distribution distance between the source and target domain data. Minimizing the kernel norm can improve the diversity of features and enhance the robustness. Finally, the effectiveness of SFCDA in multi-scene learning is proved theoretically. It is validated in three fault diagnosis scenes in four different bearing datasets. The results show that the suggested approach is more straightforward and has a better fault diagnosis effect than the state-of-the-art domain adaptive approaches.

GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations

Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is desirable. In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent Polynomial. This is facilitated by a new type of interpretable neural network block, named the “power-term approximator block”, consisting of logarithmic and exponential activation functions. GINN-LP is end-to-end differentiable, making it possible to use backpropagation for training. We propose a neural network growth strategy that will enable finding the suitable number of terms in the Laurent polynomial that represents the data, along with sparsity regularization to promote the discovery of concise equations. To the best of our knowledge, this is the first model that can discover arbitrary multivariate Laurent polynomial terms without any prior information on the order. Our approach is first evaluated on a subset of data used in SRBench, a benchmark for symbolic regression. We first show that GINN-LP outperforms the state-of-the-art symbolic regression methods on datasets generated using 48 real-world equations in the form of multivariate Laurent polynomials. Next, we propose an ensemble method that combines our method with a high-performing symbolic regression method, enabling us to discover non-Laurent polynomial equations. We achieve state-of-the-art results in equation discovery, showing an absolute improvement of 7.1% over the best contender, by applying this ensemble method to 113 datasets within SRBench with known ground-truth equations.

Improving full-waveform inversion based on sparse regularization for geophysical data

Abstract Full-waveform inversion (FWI) is an advanced geophysical inversion technique. FWI provides images of subsurface structures with higher resolution in fields such as oil exploration and geology. The conventional algorithm minimizes the misfit error by calculating the least squares of the wavefield solutions between observed data and simulated data, followed by gradient direction and model update increment. Since the gradient is calculated by forward and backward wavefields, the high-accuracy model update relies on accurate forward and backward wavefield modelling. However, the quality of wavefield solutions obtained in practical situations could be poor and does not meet the requirements of high-resolution FWI. Specifically, the low-frequency wavefield is easily affected by noise and downsampling, which influences data quality, whereas the high-frequency wavefield is susceptible to spatial aliasing effects that produce imaging artefacts. Therefore, we propose using an algorithm called sparse relaxation regularized regression to optimize the wavefield solution in frequency-domain FWI, which is the forward and backward wavefield obtained from the Helmholtz equation, thus improving FWI's accuracy. The sparse relaxation regularized regression algorithm combines sparsity and regularization, allowing the broadband FWI to reduce the effects of noise and outliers, which can provide data supplementation in the low-frequency band and anti-aliasing in the high-frequency band. Our numerical examples demonstrate the wavefield optimization effect of the sparse relaxation regularized regression-based algorithm in various cases. The improved algorithm's accuracy and stability are verified compared to the Tikhonov regularization algorithm.

How Much Can Machines Learn Finance from Chinese Text Data?

How much can we learn finance directly from text data? This paper presents a new framework for learning textual data based on the factor augmentation model and sparsity regularization, called the factor-augmented regularized model for prediction (FarmPredict), to let machines learn financial returns directly from news. FarmPredict allows the model itself to extract information directly from articles without predefined information, such as dictionaries or pretrained models as in most studies. Using unsupervised learned factors to augment the predictors would benefit our method with a “double-robust” feature: that the machine would learn to balance between individual words or text factors/topics. It also avoids the information loss of factor regression in dimensionality reduction. We apply our model to the Chinese stock market with a large proportion of retail investors by using Chinese news data to predict financial returns. We show that positive sentiments scored by our FarmPredict approach from news generate on average 83 basic points (bps) stock daily excess returns, and negative news has an adverse impact of 26 bps on the days of news announcements, where both effects can last for a few days. This asymmetric effect aligns well with the short-sale constraints in the Chinese equity market. The result shows that the machine-learned prediction does provide sizeable predictive power with an annualized return of 54% at most with a simple investment strategy. Compared with other statistical and machine learning methods, FarmPredict significantly outperforms them on model prediction and portfolio performance. Our study demonstrates the far-reaching potential of using machines to learn text data. This paper was accepted by Kay Giesecke, finance. Funding: This study was supported by the National Natural Science Foundation of China [Grants 71991471, 71991470, and 72204049], the National Key Research and Development Program [Grant 2020YFA0608604], the Shanghai Pujiang Scholar Project [Grant 21PJC010], the Shanghai Science Project [Grant 23692119300], and the China Postdoctoral Science Project [Grants 2019M650076 and 2020T130107]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01468 .

Distillation embedded absorbable pruning for fast object re-identification

Combining knowledge distillation (KD) and network pruning (NP) shows promise in learning a light network to accelerate object re-identification. However, KD requires an untrained student network to establish more critical connections in early epochs, but NP demands a well-trained student network to avoid destroying critical connections. This presents a dilemma, potentially leading to a collapse of the student network and harming object Re-ID performance. For that, we propose a distillation embedded absorbable pruning (DEAP) method. We design a pruner-convolution-pruner (PCP) unit to resolve the dilemma by loading NP’s sparse regularization on extra untrained pruners. Additionally, we propose an asymmetric relation knowledge distillation method. It readily transfers feature representation knowledge and asymmetric pairwise similarity knowledge without using additional adaptation modules. Finally, we apply re-parameterization to absorb pruners of PCP units to simplify student networks. Experiments demonstrate the superiority of DEAP, such as on the VeRi-776 dataset, with ResNet-101 as a teacher, DEAP saves 73.24% of model parameters and 71.98% of floating-point operations without sacrificing accuracy.

Structured collaborative sparse dictionary learning for monitoring of multimode processes

In this paper, a novel structured collaborative sparse dictionary learning approach is proposed to improve the monitoring performance of discriminative dictionary learning for multimode processes. The mode discriminability and data reconstruction are first balanced by decomposing the dictionary coefficients into between- and within-class parts and introducing a within-class self-expression regularization term. A weight vector of between-class coefficients is subsequently exploited for accurate mode identification of data that falls into the overlapping regions between different class distributions. Moreover, in order to pinpoint the fault variables, a scalable fault isolation method is developed which imposes a constraint of statistical control limit and introduces the ℓ1/ℓ2,0-structured sparsity regularization terms. The mode identification capability of the proposed method is proved theoretically by Theorems 1 and 2, and a lower-bound magnitude is provided by Theorem 3 for fault isolation. Finally, extensive experiments conducted in the numerical and industrial process demonstrate that our proposed method outperforms some state-of-the-art methods.

Augmented Sparse Representation for Incomplete Multiview Clustering.

Incomplete multiview data are collected from multiple sources or characterized by multiple modalities, where the features of some samples or some views may be missing. Incomplete multiview clustering (IMVC) aims to partition the data into different groups by taking full advantage of the complementary information from multiple incomplete views. Most existing methods based on matrix factorization or subspace learning attempt to recover the missing views or perform imputation of the missing features to improve clustering performance. However, this problem is intractable due to a lack of prior knowledge, e.g., label information or data distribution, especially when the missing views or features are completely damaged. In this article, we proposed an augmented sparse representation (ASR) method for IMVC. We first introduce a discriminative sparse representation learning (DSRL) model, which learns the sparse representations of multiple views as applied to measure the similarity of the existing features. The DSRL model explores complementary and consistent information by integrating the sparse regularization item and a consensus regularization item, respectively. Simultaneously, it learns a discriminative dictionary from the original samples. The sparsity constrained optimization problem in the DSRL model can be efficiently solved by the alternating direction method of multipliers (ADMM). Then, we present a similarity fusion scheme, namely, a sparsity augmented fusion of sparse representations, to obtain a sparsity augmented similarity matrix across different views for spectral clustering. Experimental results on several datasets demonstrate the effectiveness of the proposed ASR method for IMVC.