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Robust Face Recognition via Adaptive Sparse Representation

Jing Wang, Canyi Lu, Meng Wang, Peipei Li, Shuicheng Yan, Xuegang Hu

arXiv:1404.4780v1cs.CV

TL;DR

SRC can overlook correlation, while correlation-based methods can overlook sparse, discriminative sample selection. ASRC jointly models sparsity and correlation through an adaptive trace-norm representation, and experiments report strong performance across face and UCI datasets, with behavior adapting to dictionary correlation.

  • Problem

    SRC overlooks correlation information, while some correlation-aware methods overlook the discriminative sample-selection ability of sparsity in face recognition.

  • Method

    ASRC applies a trace-norm correlation adapter to the dictionary and representation vector, jointly incorporating data correlation and coefficient sparsity.

  • Results

    ASRC yields the best recognition results in most tested face-recognition cases and wins 14 of 15 comparisons with SRC on UCI datasets.

  • Takeaways & Limitations

    ASRC adapts between sparse and denser collaborative representation: it behaves like SRC with low correlation and like CRC with high correlation.

Abstract

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Sparse Representation (or coding) based Classification (SRC) has gained great success in face recognition in recent years. However, SRC emphasizes the sparsity too much and overlooks the correlation information which has been demonstrated to be critical in real-world face recognition problems. Besides, some work considers the correlation but overlooks the discriminative ability of sparsity. Different from these existing techniques, in this paper, we propose a framework called Adaptive Sparse Representation based Classification (ASRC) in which sparsity and correlation are jointly considered. Specifically, when the samples are of low correlation, ASRC selects the most discriminative samples for representation, like SRC; when the training samples are highly correlated, ASRC selects most of the correlated and discriminative samples for representation, rather than choosing some related samples randomly. In general, the representation model is adaptive to the correlation structure, which benefits from both $\ell_1$-norm and $\ell_2$-norm. Extensive experiments conducted on publicly available data sets verify the effectiveness and robustness of the proposed algorithm by comparing it with state-of-the-art methods.

I. INTRODUCTION

Face recognition remains difficult under unconstrained expressions, poses, illumination, occlusion, and limited or high-dimensional data. ASRC addresses limitations of sparse and correlation-based approaches by adapting representation to dictionary structure while jointly considering sparsity and correlation.

  • Unconstrained expressions, poses, illumination, and limited-quality images introduce occlusion, translation, and scale errors in face recognition.
  • Holistic and component-based methods represent faces globally or through patches, while feature extraction and classical classifiers provide alternative recognition pipelines.
  • SRC represents a query using an over-complete dictionary and classifies it by the smallest representation error, improving robustness to occlusions and variations.
  • SRC overlooks dictionary correlation and can become unstable with highly correlated training samples, whereas CRC uses ℓ2-norm representation but does not perform sample selection.
  • ASRC uses a trace-norm-based correlation adapter to jointly consider sparsity and correlation, adapting representation to the data structure.
  • ASRC behaves like SRC for weakly correlated samples, like CRC for highly correlated samples, and has intermediate representation sparsity in general.
  • Experiments on three face datasets and fifteen UCI datasets report ASRC as superior to existing state-of-the-art face recognition methods.

II. RELATED WORK

The related work frames face recognition as representation and classification under noise, occlusion, variation, and correlation challenges. SRC offers sparse and robust coding but assumes alignment and can ignore correlation, while CRC offers stability through denser coding but may fail to select discriminative samples when data are weakly correlated.

  • The paper reviews nearest-feature classifiers, sparse coding methods, image representation, and notation for labeled training dictionaries and query samples.
  • Figure 1 illustrates expression variation in Yale, pose variation in ORL, and illumination variation in AR face images.
  • NN uses one nearest sample, while NFL, NFP, and NFS represent a query with increasingly structured subsets or all samples from a class.
  • SRC seeks sparse coefficients over an over-complete dictionary, but its ℓ0-norm formulation is non-convex and NP-hard before relaxation for noisy data.
  • SRC assumes query and training images are well aligned and may become unstable with few samples, misalignment, or highly correlated subjects.
  • CRC replaces ℓ1-norm coding with ℓ2-norm regularization to exploit correlation, producing stable denser representations without sample selection.
  • ASRC instead combines a trace norm on the representation with the data-matrix structure and an ℓ1-norm noise term for occlusion robustness.

III. ADAPTIVE SPARSE REPRESENTATION BASED CLASSIFICATION

The method section presents an adaptive representation model that combines dictionary structure with coefficient sparsity to improve face recognition under facial variation and occlusion.

  • ASRC uses the correlation adapter || X Diag(α)||∗ to incorporate dictionary structure and coding sparsity into representation.
  • The model is designed to use sparsity for sample selection and correlation structure for relationships between the query and training samples.

A. Our Model

The model uses a trace-norm correlation adapter to jointly capture dictionary correlation and coefficient sparsity, adapting between SRC-like and CRC-like behavior.

  • A. Our Model: The correlation adapter || X Diag(α)||∗ incorporates the dictionary structure while promoting discriminative sample selection through the coding coefficients.The model applies the trace norm to the dictionary and representation vector.
  • A. Our Model: When dictionary columns are orthogonal, the correlation regularizer equals the ℓ1-norm, so the model reduces to sparse coding.This corresponds to the low-correlation case.
  • A. Our Model: When dictionary images are highly correlated, the model becomes equivalent to CRC and uses denser collaborative representation.The highly correlated case is represented by X = x1 1T and XT X = 11T.
  • A. Our Model: For intermediate dictionary structures, the resulting coefficient sparsity balances ℓ1- and ℓ2-based representations.The model’s sparsity lies between the sparsity obtained by ℓ1 and ℓ2 formulations.
  • A. Our Model: The robust formulation handles Gaussian or Laplacian corruption assumptions, with the Laplacian-based problem reported as more robust to occlusion, corruption, and variations.The formulation introduces a regularization parameter λ > 0 and is solved iteratively.

B. Optimization

The optimization reformulates the model with auxiliary variables and solves it using alternating minimization under an augmented Lagrangian framework.

  • B. Optimization: The constrained model is converted into an equivalent problem and then into an augmented Lagrange multiplier formulation.The variables J, α, and e are optimized while the other variables are fixed.
  • B. Optimization: Updating J uses the Singular Value Thresholding operator to solve its subproblem.This update is performed with α and e fixed.
  • B. Optimization: Updating α solves its subproblem while J and e are fixed.The cited optimization passage provides the corresponding α-update setup.
  • B. Optimization: Updating e uses a soft-thresholding operator, and the complete alternating procedure is given in Algorithm 1.The algorithm iterates until its convergence conditions are satisfied.

C. Adaptive Sparse Representation based Classification

ASRC codes a normalized query over the full dictionary with its adaptive correlation regularizer, then assigns the query to the class with the smallest reconstruction residual.

  • C. Adaptive Sparse Representation based Classification: ASRC normalizes dictionary columns and codes the query image over the whole dictionary using the correlation regularizer.The optimal coefficient vector is obtained with the ADM solver.
  • C. Adaptive Sparse Representation based Classification: The predicted identity is the class whose class-specific representation produces the least residual.This decision is implemented as identity(y) = arg min{ri}.
  • C. Adaptive Sparse Representation based Classification: The algorithm has time complexity O(n3).The complexity is stated for the complete recognition procedure.
  • C. Adaptive Sparse Representation based Classification: ASRC adapts its representation to dictionary structure while combining the discriminative nature of ℓ1-norm with the collaborative representation of ℓ2-norm.The stated properties identify accurate structure-dependent representation and joint benefits from both norms.
  • C. Adaptive Sparse Representation based Classification: The adaptive regularizer is described as compensating for misalignment, pixel corruption, and insufficient training samples through training-sample correlations.The authors state that this can support accurate representation even with limited samples per class.

IV. EXPERIMENTS

The experiments evaluate ASRC on real-world face databases and UCI pattern-recognition data, using PCA for face-image features and t-tests for significance.

  • IV. EXPERIMENTS: The evaluation uses Yale, ORL, and AR face-image databases together with data sets sampled from the UCI repository.The experiments assess recognition performance, robustness, and generalization ability.
  • IV. EXPERIMENTS: Table I describes 18 data sets used in the experimental evaluation.The supplied table caption identifies the table’s scope but not its individual data-set values.
  • IV. EXPERIMENTS: The study uses t-tests with significance level 0.05 to assess the statistical significance of results.PCA is adopted for feature extraction on the face-image data sets.

A. Face Recognition Without Occlusion

Across the Yale, ORL, and AR databases, ASRC consistently achieves the strongest recognition results, including when training samples are limited. Its adaptive balance of sparsity and correlation supports robust performance across differing sample conditions.

  • Robustness and mechanism: ASRC’s improvement is more pronounced with limited Yale training samples, where it captures query variations by selecting sufficient correlated training samples.Unlike CRC, ASRC also selects the most discriminative samples; with more training samples, ASRC, SRC, and CRC all perform well, but ASRC remains superior.
  • Yale database: ASRC’s maximum average accuracy on Yale rises from 75.50% at t = 2 to 94.71% at t = 7.These values are reported when the feature-space dimension reaches its largest setting.
  • Cross-database results: ASRC consistently exceeds competing methods on the Yale, ORL, and AR databases.At representative settings, ASRC reaches 76.67% on Yale, 95.58% on ORL, and 75.5% on AR, exceeding NN, NFS, SRC, CRC, and LSRC.
  • Yale database: 76.67% is ASRC’s best Yale recognition rate when t = 4, compared with 55.57% for NN and 70.86% for SRC.The same comparison reports 56.76% for NFS, 70.95% for CRC, and 71.24% for LSRC.
  • ORL database: 95.58% is ASRC’s best ORL recognition rate when t = 5, exceeding 85.7% for NN, 92.2% for NFS, 94.7% for SRC, 93.75% for CRC, and 94.00% for LSRC.ASRC remains the best-performing method across the reported ORL training levels, while all methods improve as training samples increase.
  • AR database: 75.5% is ASRC’s best AR recognition rate when t = 2, slightly above 75.25% for SRC and CRC and 74.83% for LSRC.The AR experiments use a subset with illumination and expression changes and evaluate training settings t = 2 and t = 7.

B. Face Recognition Despite Random Pixel Corruption

ASRC remains robust as random pixel corruption increases across Yale, ORL, and AR face databases. Its adaptive use of correlation information complements sparse representation, helping compensate for corrupted query-image regions.

  • The evaluation corrupts randomly selected test-image pixels with independent uniform-distribution samples, varying corruption from 10% to 80%.Yale uses six training images per subject, while ORL and AR use half their images for training.
  • ASRC recognizes Yale subjects above 80% from 0% to 20% occlusion and exceeds competitors by over 10% at 30% to 40% occlusion.At roughly 50% to 60% occlusion, it still achieves the best recognition rates, at least 3% higher than competitors.
  • On ORL, ASRC exceeds 85% recognition from 0% to 30% occlusion, reaches 78% at 40% corruption, and remains above 60% at 50% occlusion.
  • On AR, ASRC and SRC achieve around 80% recognition from 0% to 40% occlusion, outperforming the other compared methods.At some higher-corruption settings, LSRC or SRC is slightly higher than ASRC, but the difference is not statistically significant.
  • Correlation information can compensate corrupted query-image regions, while SRC’s ℓ1-minimization requires a large sum of training samples.

C. Experimental Results on UCI Data Sets

Experiments on 15 UCI data sets show that ASRC performs strongly across general pattern-recognition tasks. It outperforms NFS everywhere and beats SRC, NN, and SVM in most comparisons, while CRC is higher on three data sets without statistically significant differences.

  • The UCI evaluation uses 10-fold cross-validation and records mean and standard deviation of accuracy across 15 data sets.
  • ASRC outperforms NFS on all 15 UCI data sets and wins against SRC 14 times, except on German by 0.2%.
  • ASRC wins against NN 12 times and ties once on X8D5K.
  • CRC has higher accuracy than ASRC on three data sets, but the differences are not statistically significant.
  • SVM obtains the best results overall among the compared methods but remains inferior to ASRC in eight comparisons.

V. CONCLUSION

The conclusion presents ASRC as an adaptive classifier that jointly uses sparsity and correlation for face recognition. Its behavior ranges from SRC-like under low correlation to CRC-like under high correlation, while experiments support effectiveness and robustness.

  • ASRC jointly considers sparsity and correlation, selecting samples that are both discriminative and related to the dictionary structure.
  • With low dictionary correlation, ASRC obtains results comparable to SRC; with high correlation, it performs as well as CRC.
  • In intermediate cases, ASRC forms a linear representation from the most related and discriminative samples.
  • Experiments on real-world face-image data sets report that ASRC outperforms methods including SVM, NN, NFS, SRC, and CRC in recognition precision and robustness.
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