Pith. sign in

REVIEW 3 major objections 7 minor 63 references

Non-negative Sparse and Collaborative Representation for Pattern Classification

T0 review · 3 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that forcing representation coefficients to be non-negative, while keeping both sparse and collaborative penalties, produces a classifier that beats earlier representation classifiers and even strong deep baselines on…

desk verdict A correct but incremental combination of non-negativity with elastic net for representation classification, undermined by a missing ablation and an overblown deep-learning claim. read the letter →

arxiv 1908.07956 v3 pith:47BKMAL7 submitted 2019-08-20 cs.CV

Jun Xu , Zhou Xu , Wangpeng An , Haoqian Wang , David Zhang This is my paper · ORCID
classification cs.CV MSC 68T10
keywords non-negativerepresentationsparsecollaborativepatternclassificationfacerecognitionfine-grainedvisualelasticnetADMM
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that forcing the coefficients of a representation-based classifier to be non-negative, while keeping both sparse ($\ell^1$) and collaborative ($\ell^2$) penalties, makes the coding vector more discriminative and physically meaningful, and that a classifier built on this representation beats earlier sparse, collaborative, and non-negative representation classifiers as well as strong deep baselines on several benchmarks. The target is a single optimization problem, minimize $\|y-Xc\|_2^2+\alpha\|c\|_2^2+\beta\|c\|_1$ subject to $c\ge 0$, whose solution codes a test image as an additive combination of training images. If the claim holds, a simple linear coding step can replace heavier machinery on tasks like fine-grained visual classification without sacrificing accuracy. The paper's evidence is a set of comparisons on face, digit, action, object, and fine-grained datasets. A sympathetic reader would take the central assertion to be: non-negativity is not a minor constraint but the ingredient that removes canceling negative coefficients and sharpens the class-specific residual.

What carries the argument

The central object is the NSCR model in Eq. (4)-(5): $\min_c\|y-Xc\|_2^2+\alpha\|c\|_2^2+\beta\mathbf{1}^\top c$ subject to $c\ge 0$. It is a non-negatively constrained elastic net: the $\ell^2$ term induces the collaborative, dense-over-classes behavior of CRC, the $\ell^1$ term (re-expressed as $\beta\mathbf{1}^\top c$ because $c\ge 0$) induces sparsity, and the non-negativity constraint forbids subtractive cancellations. The optimization machinery is ADMM with variable splitting $z=c$, producing the closed-form updates in Algorithm 1, with the Woodbury identity used to reduce the per-iteration inversion cost from $O(N^3)$ to $O(DN^2)$.

What would settle it

Take a dataset where each class's training samples lie on a low-dimensional subspace but the test samples are generated outside the positive cone of those samples (for example, by subtracting a class-specific pattern or by applying a global shift that makes some coordinates negative). If NSCR's accuracy drops to the level of random guessing while an unconstrained $\ell^2$ classifier stays accurate, the claim that non-negativity helps would be shown to depend entirely on the cone assumption. A simpler check: on any benchmark, compare NSCR against its own unconstrained version with identical $\alpha,\beta$; if accuracy is not systematically higher, the paper's central claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the non-negative sparse and collaborative representation (NSCR), obtained by adding the constraint $c\ge 0$ to the elastic-net style objective $\min_c \|y-Xc\|_2^2+\alpha\|c\|_2^2+\beta\|c\|_1$, produces coding vectors that are globally sparse, locally dense, and additive rather than subtractive, and that the residual classifier $\arg\min_k\|y-X_k\hat{c}_k\|_2$ built on these codes is more accurate than SRC, CRC, ProCRC, NRC, and, in reported comparisons, the bilinear CNN (B-CNN) baseline on fine-grained datasets. The authors identify the reason as physical meaningfulness: allowing negative coefficients lets training images cancel one another, which is mathematically valid but not a faithful generative account; non-negativity restricts reconstruction to the additive cone and thereby makes the coefficients more interpretable and the residuals more class-selective. The paper also claims the optimization is tractable: an ADMM scheme with closed-form updates for each subproblem, with complexity $O(DN^2T)$, and convergence to the global optimum because the objective is strictly convex.

Load-bearing premise

The classifier assumes every test sample can be closely approximated by an additive, non-negative combination of the training samples of its own class; if a test sample falls outside that non-negative cone, its class residual will not reliably identify the label.

Editorial extensions

If this is right

  • A single non-negativity constraint upgrades the classic SRC/CRC residual classifier and matches or exceeds much heavier CNN classifiers on fine-grained tasks, suggesting linear coding still has headroom when constrained correctly.
  • The classifier inherits elastic-net flexibility: the two parameters $\alpha$ and $\beta$ trade collaboration against sparsity, and the reported parameter analysis indicates accuracy is stable over wide ranges.
  • The closed-form ADMM updates and precomputable matrix inverse make the method practical at large training-set sizes, with overall complexity $O(DN^2T)$.
  • For representation-based classifiers, the paper implies that the coding vector's sign pattern, not just its magnitude or sparsity, is a major source of discriminative power.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not analyze when the non-negative cone assumption holds; one testable extension is to characterize class geometries (for example, convex hull membership) under which the residual rule is provably correct, and to measure how accuracy degrades as test samples leave the cone.
  • Because the non-negative constraint turns the $\ell^1$ penalty into a linear term, NSCR may be viewed as a parameterized interpolation between non-negative least squares and ridge-style collaboration; this suggests connections to cone-projection geometry and to non-negative matrix factorization, though the paper does not develop them.
  • The reported gains over B-CNN on fine-grained sets, if they replicate, imply that a representation step applied to VGG features can substitute for end-to-end fine-tuning in some regimes; a direct test would be combining NSCR with stronger modern features.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper proposes NSCR, a representation-based classifier that represents a test sample as a non-negative linear combination of training samples while jointly applying l1 and l2 regularization on the coding vector. The objective is given in Eq. (4), and an ADMM algorithm with closed-form updates is derived in Section 3.2. Classification is performed by assigning the test sample to the class with the smallest reconstruction residual. Experiments on face, digit, object, action, and fine-grained classification datasets compare NSCR against SRC, CRC, CROC, ProCRC, NRC, SVM, and occasionally the B-CNN deep baseline. The paper claims that NSCR outperforms previous sparse/collaborative/non-negative representation classifiers as well as state-of-the-art deep approaches.

Significance. The optimization part of the paper is sound: the c-, z-, and delta-updates in Eqs. (9)-(13) are algebraically correct, the Woodbury identity is applied in a standard way, and the complexity estimate O(D N^2 T) is reasonable. The experimental coverage is broad, and the reported accuracies are mostly higher than those of the compared non-deep baselines. However, the central attribution of the gains to the non-negativity constraint is not tested, because no unconstrained elastic-net baseline is reported. The margins over NRC are often small and are not accompanied by standard deviations or significance tests. The comparison to 'state-of-the-art deep approaches' rests on a single 2015 B-CNN baseline, and the feature protocol for that comparison is ambiguous. If the missing ablation is added and the claims are appropriately toned down, the result would be a useful incremental contribution; as it stands, the main claim is not fully supported.

major comments (3)
  1. [§3.1, Eq. (4) and Tables 1-10] The proposed objective is a non-negative elastic net, yet no unconstrained elastic-net baseline is reported. SRC uses only the l1 penalty, CRC only the l2 penalty, and NRC only the constraint c>=0; none of these isolates the effect of adding c>=0 to the joint l1+l2 penalty. As a result, the gains over NRC (which are only 0.3 to 0.9 percentage points in several tables, e.g., Tables 5-8) could be caused entirely by the regularization terms rather than by the non-negativity that the title and Section 1 identify as the source of the improvement. This missing control is load-bearing for the central claim. Please add an ablation with the same alpha and beta but without the non-negativity constraint, and ideally also non-negative l2-only and non-negative l1-only variants.
  2. [§4.4-§4.8, Tables 1-10] The experimental reporting is insufficient to support the claimed improvements. Tables 1, 5, 7, 8, 9, and 10 do not state the number of random trials, and Tables 2, 3, 4, and 6, which say 'averaged on 10 independent trials,' do not report standard deviations. Because the margins over NRC are often small (e.g., 82.3 vs 81.9 in Table 5 VGG19, 86.0 vs 85.6 in Table 6, 79.5 vs 79.0 in Table 7), the reported differences may be within run-to-run variability. Please report mean plus/minus standard deviation over at least 10 random splits for every table and add paired significance tests (e.g., Wilcoxon signed-rank) for the comparisons to NRC and the other main baselines.
  3. [Abstract and §4.8, Tables 9-10] The claim that NSCR 'outperforms ... state-of-the-art deep approaches' is not supported as stated. The only deep baseline is B-CNN [60], a 2015 method, and no modern fine-tuned CNN baseline is included. Moreover, the feature protocol in these tables is ambiguous: the text says 'The features are extracted by using a VGG-16 network [3] by end-to-end manner,' but NSCR is not an end-to-end classifier. Please clarify what features NSCR receives in Tables 9-10, whether B-CNN is fine-tuned, and either add stronger deep baselines or revise the abstract to say 'a deep baseline.'
minor comments (7)
  1. [§2 and §3.2] There are two algorithms labeled 'Algorithm 1': the SRC/CRC/NRC algorithm in Section 2 and the NSCR-ADMM solver in Section 3.2. Renumber the ADMM solver as Algorithm 2 and the NSCR classifier as Algorithm 3.
  2. [Eq. (12)] Equation (12) has a typo: 'zt+1 = max(0,ck+1−ρ−1δt))' should be 'z^{t+1} = max(0, c^{t+1} − ρ^{−1} δ^t)', without the extra parenthesis and with c^{t+1} in place of ck+1.
  3. [§4.4, Table 2] The text says results are reported for d = 84, 120, 300, but Table 2 lists d = 84, 150, 300; the two should be made consistent.
  4. [§4.1 and Algorithm 1] Section 4.1 lists 'iteration number K' as a parameter, while Algorithm 1 uses T for the maximal iteration count; unify the notation.
  5. [§4.8, Tables 9-10] The text says NSCR is 0.7% higher than ProCRC and 0.2% higher than B-CNN, but the table values imply 1.0 and 0.5 percentage-point differences, respectively; also, 'present' should be 'percent.'
  6. [Figure 3] Figure 3 has no axis labels and the vertical axes are not clearly scaled; add axis labels, a legend, and consistent tick marks so the parameter analysis can be read.
  7. [§3.2] The text says a convergence analysis is given, but the subsection only asserts convexity and shows a plot; a short argument citing standard ADMM convergence results would make the statement accurate.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the sole self-citation (NRC) is a baseline and does not force the result.

full rationale

The paper's derivation chain is an optimization model (Eq. 4) plus a residual-based classification rule (Algorithm 2), and the reported accuracy is obtained by evaluating that rule on held-out test data. The parameters α and β are selected by 5-fold cross-validation on training sets, which is standard model selection rather than a fitted input renamed as a prediction. The central claim that NSCR outperforms SRC/CRC/NRC is supported by the paper's own experiments in Section 4, not by a self-citation. The only self-citation is NRC [22], which shares authors with this paper; it is used as a comparison baseline and as motivation that non-negativity aids discriminative representation, but the NSCR-versus-NRC comparison is independently tested, so that citation is not load-bearing. The paper explicitly acknowledges that Eq. (4) is a non-negative constrained elastic LASSO [26], so the model is not presented as a derivation from inputs that collapse into the conclusion. The absence of an ablation that removes the c ≥ 0 constraint is an experimental attribution weakness, not a circularity; it means the gains over NRC could in principle come from the elastic-net regularization. Because the remaining self-citation is minor and non-load-bearing, the analysis is a non-finding on circularity, scored at the mild end of the scale.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The model relies on standard regularization assumptions and the linear reconstruction assumption. No novel entities are introduced. Two per-dataset regularization parameters are tuned via cross-validation, plus a fixed ADMM penalty parameter.

free parameters (3)
  • Regularization parameter alpha = 0.01, 0.05, or 0.1 depending on dataset
    Controls l2 penalty in Eq. (4); chosen by 5-fold cross-validation on each training set, values reported per dataset in Section 4.
  • Regularization parameter beta = 0.01, 0.05, or 0.1 depending on dataset
    Controls l1 penalty in Eq. (4); chosen by 5-fold cross-validation on each training set.
  • ADMM penalty parameter rho = 10
    Fixed hand-set value in Algorithm 1, not tuned; robustness to rho is not analyzed.
assumptions (3)
  • domain assumption A test sample can be approximated as a non-negative linear combination of same-class training samples, so residual ||y - X_k c_k||_2 is a valid class discriminator.
    This underlies the residual labeling rule in Algorithm 2 and is the premise that representation-based classifiers inherit. No verification of the non-negative cone condition is given.
  • standard math Strict convexity of the NSCR objective guarantees global convergence of ADMM.
    Invoked in Section 3.2; holds for alpha greater than 0. The paper relies on Boyd et al.'s ADMM convergence theory.
  • domain assumption Non-negative combinations are more physically reasonable for image reconstruction than signed combinations.
    Stated in Sections 1 and 3.1 citing NMF literature; used to motivate the model but not strictly load-bearing for the classification comparison.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Non-negative Sparse and Collaborative Representation for Pattern Classification." pith.science (2026). https://pith.science/paper/47BKMAL7

@misc{pith2026190807956,
  author       = {Pith},
  title        = {Pith review of: Non-negative Sparse and Collaborative Representation for Pattern Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/47BKMAL7}},
  note         = {Machine review of arXiv:1908.07956}
}
read the original abstract

Sparse representation (SR) and collaborative representation (CR) have been successfully applied in many pattern classification tasks such as face recognition. In this paper, we propose a novel Non-negative Sparse and Collaborative Representation (NSCR) for pattern classification. The NSCR representation of each test sample is obtained by seeking a non-negative sparse and collaborative representation vector that represents the test sample as a linear combination of training samples. We observe that the non-negativity can make the SR and CR more discriminative and effective for pattern classification. Based on the proposed NSCR, we propose a NSCR based classifier for pattern classification. Extensive experiments on benchmark datasets demonstrate that the proposed NSCR based classifier outperforms the previous SR or CR based approach, as well as state-of-the-art deep approaches, on diverse challenging pattern classification tasks.

Figures

Figures reproduced from arXiv: 1908.07956 by the authors.

Figure 1
Figure 1. An illustrative comparison of the coding vectors obtained by SRC [2], CRC [13], [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The convergence curves of kct+1 − zt+1k2 (red line), kzt+1 − ztk2 (blue line), and kct+1 − ctk2 (green line) of the proposed NSCR model (6) on Extended Yale B [49]. Algorithm 2: The NSCR based Classifier Input: Query sample y, training image matrix X = [X1, ..., XK], tolerance value Tol > 0, maximal iteration number T, regularization parameters α, β, and penalty parameter ρ > 0; 1. Normalize the columns of X to have… view at source ↗
Figure 3
Figure 3. We observe that the proposed NSCR model is very robust on the [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: Classification accuracy of NSCR with different parameters [PITH_FULL_IMAGE:figures/full_fig_p021_3.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 60 canonical work pages

  1. [60]

    Bilinear cnn models for fine-grained visual recognition

    Tsung-Yu Lin, Aruni RoyChowdhury, and Subhransu Maji. Bilinear cnn models for fine-grained visual recognition. In Proceedings of the IEEE International Conference on Computer Vision , pages 1449–1457, 2015

    work page 2015

  2. [3]

    A probabilistic collaborative representation based approach for pattern classification

    Sijia Cai, Lei Zhang, Wangmeng Zuo, and Xiangchu Feng. A probabilistic collaborative representation based approach for pattern classification. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages 2950–2959, 2016

    work page 2016

  3. [1]

    L. J. Li and Li Fei-Fei. What, where and who? classifying events by scene and object recognition. International Conference on Computer Vision , pages 1–8, 2007

    work page 2007

  4. [2]

    Wright, A

    J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence , 31(2):210–227, 2009

    work page 2009

  5. [4]

    Cross version defect prediction with representative data via sparse subset selection

    Zhou Xu, Shuai Li, Yutian Tang, Xiapu Luo, Tao Zhang, Jin Liu, and Jun Xu. Cross version defect prediction with representative data via sparse subset selection. In Proceedings of the 26th Conference on Program Comprehension , pages 132–143. ACM, 2018

    work page 2018

  6. [5]

    Tstss: A two-stage training subset selection framework for cross version defect prediction

    Zhou Xu, Shuai Li, Xiapu Luo, Jin Liu, Tao Zhang, Yutian Tang, Jun Xu, Peipei Yuan, and Jacky Keung. Tstss: A two-stage training subset selection framework for cross version defect prediction. Journal of Systems and Software , 154:59–78, 2019

    work page 2019

  7. [6]

    Statistical learning theory, volume 1

    Vladimir Naumovich Vapnik and Vlamimir Vapnik. Statistical learning theory, volume 1. Wiley New York, 1998

    work page 1998

  8. [7]

    Acquiring linear subspaces for face recog- nition under variable lighting

    Kuang-Chih Lee, Jeffrey Ho, and David J Kriegman. Acquiring linear subspaces for face recog- nition under variable lighting. IEEE Transactions on Pattern Analysis and Machine Intelligence , 27(5):684–698, 2005

    work page 2005

Show all 63 references
  1. [8]

    Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories

    Svetlana Lazebnik, Cordelia Schmid, and Jean Ponce. Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 2169–2178. IEEE, 2006

    2006

  2. [9]

    Linear spatial pyramid matching using sparse coding for image classification

    Jianchao Yang, Kai Yu, Yihong Gong, and Thomas Huang. Linear spatial pyramid matching using sparse coding for image classification. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1794–1801. IEEE, 2009

    2009

  3. [10]

    S. Gao, I. W. H. Tsang, L. T. Chia, and P. Zhao. Local features are not lonely-laplacian sparse coding for image classification. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 3555–3561, 2010

    2010

  4. [11]

    Discriminative k-svd for dictionary learning in face recognition

    Qiang Zhang and Baoxin Li. Discriminative k-svd for dictionary learning in face recognition. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 2691–2698. IEEE, 2010

    2010

  5. [12]

    Fisher discrimination dictionary learning for sparse representation

    Meng Yang, Lei Zhang, Xiangchu Feng, and David Zhang. Fisher discrimination dictionary learning for sparse representation. In IEEE International Conference on Computer Vision (ICCV) , pages 543–550. IEEE, 2011. 22

    2011

  6. [13]

    Sparse representation or collaborative representation: Which helps face recognition? IEEE international conference on Computer vision (ICCV) , pages 471–478, 2011

    Lei Zhang, Meng Yang, and Xiangchu Feng. Sparse representation or collaborative representation: Which helps face recognition? IEEE international conference on Computer vision (ICCV) , pages 471–478, 2011

    2011

  7. [14]

    Imagenet classification with deep convo- lutional neural networks

    Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convo- lutional neural networks. In Advances in Neural Information Processing Systems (NIPS) , pages 1097–1105, 2012

    2012

  8. [15]

    Kernel sparse representation-based classifier

    Li Zhang, Wei-Da Zhou, Pei-Chann Chang, Jing Liu, Zhe Yan, Ting Wang, and Fan-Zhang Li. Kernel sparse representation-based classifier. IEEE Transactions on Signal Processing , 60(4):1684– 1695, 2012

    2012

  9. [16]

    Jiang, Z

    Z. Jiang, Z. Lin, and L. S. Davis. Label consistent k-svd: Learning a discriminative dictionary for recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence , 35(11):2651–2664, 2013

    2013

  10. [17]

    Classification and boosting with multiple collaborative representations

    Yuejie Chi and Fatih Porikli. Classification and boosting with multiple collaborative representations. IEEE Transactions on Pattern Analysis and Machine Intelligence , 36(8):1519–1531, 2014

    2014

  11. [18]

    T. H. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng, and Y. Ma. Pcanet: A simple deep learning baseline for image classification? IEEE Transactions on Image Processing , 24(12):5017–5032, 2015

    2015

  12. [19]

    Deep residual learning for image recog- nition

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 770–778, 2016

    2016

  13. [20]

    Weinberger

    Gao Huang, Zhuang Liu, Laurens van der Maaten, and Kilian Q. Weinberger. Densely connected convolutional networks. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), July 2017

    2017

  14. [21]

    Squeeze-and-excitation networks

    Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , June 2018

    2018

  15. [22]

    Sparse, collaborative, or nonnegative repre- sentation: Which helps pattern classification? Pattern Recognition, 88:679 – 688, 2019

    Jun Xu, Wangpeng An, Lei Zhang, and David Zhang. Sparse, collaborative, or nonnegative repre- sentation: Which helps pattern classification? Pattern Recognition, 88:679 – 688, 2019

    2019

  16. [23]

    Learning the parts of objects by non-negative matrix factor- ization

    Daniel D Lee and H Sebastian Seung. Learning the parts of objects by non-negative matrix factor- ization. Nature, 401(6755):788–791, 1999

    1999

  17. [24]

    Why is facial occlusion a challenging problem? In Advances in Biometrics: Third International Conference , pages 299–308, Berlin, Heidelberg, 2009

    Hazım Kemal Ekenel and Rainer Stiefelhagen. Why is facial occlusion a challenging problem? In Advances in Biometrics: Third International Conference , pages 299–308, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg

    2009

  18. [25]

    Rigamonti, M

    R. Rigamonti, M. A. Brown, and V. Lepetit. Are sparse representations really relevant for image classification? In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , pages 1545–1552, 2011

    2011

  19. [26]

    Regularization and variable selection via the elastic net

    Hui Zou and Trevor Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 67(2):301–320, 2005

    2005

  20. [27]

    Regression shrinkage and selection via the lasso

    Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) , pages 267–288, 1996

    1996

  21. [28]

    Gradient-based learning applied to document recognition

    Yann LeCun, L´ eon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE , 86(11):2278–2324, 1998. 23

    1998

  22. [29]

    Bruna and S

    J. Bruna and S. Mallat. Invariant scattering convolution networks. IEEE Transactions on Pattern Analysis and Machine Intelligence , 35(8):1872–1886, 2013

    2013

  23. [30]

    S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn., 3(1):1–122, January 2011

    2011

  24. [31]

    Nearest neighbor pattern classification

    T Cover and P Hart. Nearest neighbor pattern classification. IEEE Transaction on Information Theory, 13(1):21–27, 1953

    1953

  25. [32]

    Lee and H Sebastian Seung

    Daniel D. Lee and H Sebastian Seung. Algorithms for non-negative matrix factorization. in nips. Advances in Neural Information Processing Systems , 13(6):556–562, 2000

    2000

  26. [33]

    J. Yang, C. Liu, and L. Zhang. Color space normalization: Enhancing the discriminating power of color spaces for face recognition. Pattern Recognition, 43(4):1454 – 1466, 2010

    2010

  27. [34]

    J. Yang, L. Zhang, Y. Xu, and J. Yang. Beyond sparsity: The role of 𝓁1-optimizer in pattern classification. Pattern Recognition, 45(3):1104 – 1118, 2012

    2012

  28. [35]

    M. Yang, Z. Feng, C.K. Shiu, and L. Zhang. Fast and robust face recognition via coding residual map learning based adaptive masking. Pattern Recognition, 47(2):535 – 543, 2014

    2014

  29. [36]

    J. Xie, L. Zhang, J. You, and S. Shiu. Effective texture classification by texton encoding induced statistical features. Pattern Recognition, 48(2):447–457, 2015

    2015

  30. [37]

    Z. Feng, M. Yang, L. Zhang, Y. Liu, and D. Zhang. Joint discriminative dimensionality reduction and dictionary learning for face recognition. Pattern Recognition, 46(8):2134 – 2143, 2013

    2013

  31. [38]

    G. Lin, M. Yang, J. Yang, L. Shen, and W. Xie. Robust, discriminative and comprehensive dictionary learning for face recognition. Pattern Recognition, 81:341 – 356, 2018

    2018

  32. [39]

    Timofte and L

    R. Timofte and L. Van Gool. Adaptive and weighted collaborative representations for image classi- fication. Pattern Recognition Letters, 43:127–135, 2014

    2014

  33. [40]

    Gosselin, N

    P. Gosselin, N. Murray, H. J´ egou, and F. Perronnin. Revisiting the fisher vector for fine-grained classification. Pattern Recognition Letters, 49:92–98, 2014

    2014

  34. [41]

    Discriminative collab- orative representation for classification

    Yang Wu, Wei Li, Masayuki Mukunoki, Michihiko Minoh, and Shihong Lao. Discriminative collab- orative representation for classification. In Asian Conference on Computer Vision , pages 205–221, 2014

    2014

  35. [42]

    The why and how of nonnegative matrix factorization

    Nicolas Gillis. The why and how of nonnegative matrix factorization. Regularization, Optimization, Kernels, and Support Vector Machines , 12(257), 2014

    2014

  36. [43]

    Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization

    Martin Slawski and Matthias Hein. Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization. Electron. J. Statist. , 7:3004–3056, 2013

    2013

  37. [44]

    Better subset regression using the nonnegative garrote

    Leo Breiman. Better subset regression using the nonnegative garrote. Technometrics, 37(4):373–384, 1995

    1995

  38. [45]

    Hierarchical als algorithms for nonnegative matrix and 3d tensor factorization

    Andrzej Cichocki, Rafal Zdunek, and Shun Ichi Amari. Hierarchical als algorithms for nonnegative matrix and 3d tensor factorization. Springer Lncs , 4666:169–176, 2007

    2007

  39. [46]

    R. Courant. Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc. , 49(1):1–23, 1943. 24

    1943

  40. [47]

    Eckstein and D

    J. Eckstein and D. P. Bertsekas. On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55(1):293–318, 1992

    1992

  41. [48]

    K. Riedel. A sherman-morrison-woodbury identity for rank augmenting matrices with application to centering. SIAM Journal on Matrix Analysis and Applications , 13(2):659–662, 1992

    1992

  42. [49]

    Georghiades, P.N

    A.S. Georghiades, P.N. Belhumeur, and D.J. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence , 23(6):643–660, 2001

    2001

  43. [50]

    Martinez and R

    A.M. Martinez and R. Benavente. The ar face database. CVC Technical Report No. 24 , 1998

    1998

  44. [51]

    Jonathan J. Hull. A database for handwritten text recognition research. IEEE Transactions on Pattern Analysis and Machine Intelligence , 16(5):550–554, 1994

    1994

  45. [52]

    Human action recognition by learning bases of action attributes and parts

    Bangpeng Yao, Xiaoye Jiang, Aditya Khosla, Andy Lai Lin, Leonidas Guibas, and Li Fei-Fei. Human action recognition by learning bases of action attributes and parts. In Computer Vision (ICCV), 2011 IEEE International Conference on , pages 1331–1338. IEEE, 2011

    2011

  46. [53]

    Caltech-256 object category dataset

    Gregory Griffin, Alex Holub, and Pietro Perona. Caltech-256 object category dataset. 2007

    2007

  47. [54]

    The caltech-ucsd birds-200-2011 dataset

    Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-ucsd birds-200-2011 dataset. 2011

    2011

  48. [55]

    Nilsback and A

    M-E. Nilsback and A. Zisserman. Automated flower classification over a large number of classes. In Proceedings of the Indian Conference on Computer Vision, Graphics and Image Processing , Dec 2008

    2008

  49. [56]

    Fine-grained visual classification of aircraft

    Subhransu Maji, Esa Rahtu, Juho Kannala, Matthew Blaschko, and Andrea Vedaldi. Fine-grained visual classification of aircraft. arXiv preprint arXiv:1306.5151 , 2013

    2013 arXiv

  50. [57]

    3d object representations for fine-grained categorization

    Jonathan Krause, Michael Stark, Jia Deng, and Li Fei-Fei. 3d object representations for fine-grained categorization. In Proceedings of the IEEE International Conference on Computer Vision Work- shops, pages 554–561, 2013

    2013

  51. [58]

    Liblinear: A library for large linear classification

    Rong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, Xiang-Rui Wang, and Chih-Jen Lin. Liblinear: A library for large linear classification. Journal of Machine Learning Research , 9(Aug):1871–1874, 2008

    2008

  52. [59]

    Symbiotic segmentation and part local- ization for fine-grained categorization

    Yuning Chai, Victor Lempitsky, and Andrew Zisserman. Symbiotic segmentation and part local- ization for fine-grained categorization. In Proceedings of the IEEE International Conference on Computer Vision , pages 321–328, 2013

    2013

  53. [61]

    Vlfeat: An open and portable library of computer vision algorithms

    Andrea Vedaldi and Brian Fulkerson. Vlfeat: An open and portable library of computer vision algorithms. In Proceedings of the 18th ACM International Conference on Multimedia , pages 1469–

  54. [62]

    Distinctive image features from scale-invariant keypoints

    David G Lowe. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision , 60(2):91–110, 2004

    2004

  55. [63]

    Very deep convolutional networks for large-scale image recognition

    Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In International Conference on Learning Representations (ICLR) , 2014. 25

    2014

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.