Abstract
This paper focuses on efficient algorithms for single and multi-view spectral clustering with a convex regularization term for very large scale image datasets. In computer vision applications, multiple views denote distinct image-derived feature representations that inform the clustering. Separately, the regularization encodes high level advice such as tags or user interaction in identifying similar objects across examples. Depending on the specific task, schemes to exploit such information may lead to a smooth or non-smooth regularization function. We present stochastic gradient descent methods for optimizing spectral clustering objectives with such convex regularizers for datasets with up to a hundred million examples. We prove that under mild conditions the local convergence rate is \(O(1/\sqrt{T})\) where T is the number of iterations; further, our analysis shows that the convergence improves linearly by increasing the number of threads. We give extensive experimental results on a range of vision datasets demonstrating the algorithm’s empirical behavior.
Chapter PDF
References
Balzano, L., Nowak, R., Recht, B.: Online identification and tracking of subspaces from highly incomplete information. In: Proceedings of the Allerton Conference on Communication, Control and Computing (2010)
Batra, D., Agrawal, H., Banik, P., Chavali, N., Alfadda, A.: CloudCV: Large-scale distributed computer vision as a cloud service (2013), http://www.cloudcv.org
Bay, H., Tuytelaars, T., Van Gool, L.: Surf: Speeded up robust features. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006, Part I. LNCS, vol. 3951, pp. 404–417. Springer, Heidelberg (2006)
Bickel, S., Scheffer, T.: Multi-view clustering. In: Proceedings of the IEEE International Conference on Data Mining (2004)
Blaschko, M.B., Lampert, C.H.: Correlational spectral clustering. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2008)
Chaudhuri, K., Kakade, S.M., Livescu, K., Sridharan, K.: Multi-view clustering via canonical correlation analysis. In: Proceedings of the International Conference on Machine Learning (2009)
Chen, W., Song, Y., Bai, H., Lin, C., Chang, E.Y.: Parallel spectral clustering in distributed systems. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(3), 568–586 (2011)
Chen, X., Cai, D.: Large scale spectral clustering with landmark-based representation. In: Proceedings of the AAAI Conference on Artificial Intelligence (2011)
Darken, C., Moody, J.: Towards faster stochastic gradient search. In: Advances in Neural Information Processing Systems (1993)
Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: ImageNet: A Large-Scale Hierarchical Image Database. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2009)
Donahue, J., Jia, Y., Vinyals, O., Hoffman, J., Zhang, N., Tzeng, E., Darrell, T.: Decaf: A deep convolutional activation feature for generic visual recognition. ArXiv preprint ArXiv:1310.1531 (2013)
Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM Journal on Matrix Analysis and Applications 20(2), 303–353 (1998)
Fowlkes, C., Belongie, S., Chung, F., Malik, J.: Spectral grouping using the Nyström method. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 214–225 (2004)
Gehler, P., Nowozin, S.: On feature combination for multiclass object classification. In: Proceedings of the IEEE International Conference on Computer Vision (2009)
Hofmann, T.: Probabilistic latent semantic analysis. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence (1999)
Khoa, N.L.D., Chawla, S.: Large scale spectral clustering using resistance distance and Spielman-Teng solvers. In: Ganascia, J.-G., Lenca, P., Petit, J.-M. (eds.) DS 2012. LNCS, vol. 7569, pp. 7–21. Springer, Heidelberg (2012)
Krishnamurthy, A., Balakrishnan, S., Xu, M., Singh, A.: Efficient active algorithms for hierarchical clustering. In: Proceedings of the International Conference on Machine Learning (2012)
Kulis, B., Grauman, K.: Kernelized locality-sensitive hashing for scalable image search. In: Proceedings of the IEEE International Conference on Computer Vision (2009)
Kumar, A., Daumé III, H.: A co-training approach for multi-view spectral clustering. In: Proceedings of the International Conference on Machine Learning (2011)
Kumar, A., Rai, P., Daumé III, H.: Co-regularized multi-view spectral clustering. In: Advances in Neural Information Processing Systems (2011)
Lazebnik, S., Schmid, C., Ponce, J.: Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2006)
Lehoucq, R.B., Sorensen, D.C., Yang, C.: ARPACK users’ guide: Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, vol. 6 (1998)
Li, L., Su, H., Xing, E.P., Fei-Fei, L.: Object bank: A high-level image representation for scene classification & semantic feature sparsification. In: Advances in Neural Information Processing Systems (2010)
Li, M., Lian, X.C., Kwok, J., Lu, B.L.: Time and space efficient spectral clustering via column sampling. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2011)
Liu, J., Wang, C., Gao, J., Han, J.: Multi-view clustering via joint nonnegative matrix factorization. In: SIAM International Conference on Data Mining (2013)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)
Oliva, A., Torralba, A.: Modeling the shape of the scene: A holistic representation of the spatial envelope. International Journal of Computer Vision 42(3), 145–175 (2001)
Sakai, T., Imiya, A.: Fast spectral clustering with random projection and sampling. In: Machine Learning and Data Mining in Pattern Recognition (2009)
Serre, T., Wolf, L., Poggio, T.: Object recognition with features inspired by visual cortex. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2005)
Tang, W., Lu, Z., Dhillon, I.S.: Clustering with multiple graphs. In: Proceedings of the IEEE International Conference on Data Mining (2009)
Torralba, A., Fergus, R., Freeman, W.T.: 80 million tiny images: a large dataset for non-parametric object and scene recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(11), 1958–1970 (2008)
Tuzel, O., Porikli, F., Meer, P.: Region covariance: A fast descriptor for detection and classification. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 589–600. Springer, Heidelberg (2006)
Wen, Z., Yin, W.: A feasible method for optimization with orthogonality constraints. Mathematical Programming, 1–38 (2012)
Xu, J., Ithapu, V.K., Mukherjee, L., Rehg, J.M., Singh, V.: GOSUS: Grassmannian Online Subspace Updates with Structured-sparsity. In: Proceedings of the IEEE International Conference on Computer Vision (2013)
Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: Advances in Neural Information Processing Systems (2004)
Zhou, D., Burges, C.J.C.: Spectral clustering and transductive learning with multiple views. In: Proceedings of the International Conference on Machine Learning (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Collins, M.D., Liu, J., Xu, J., Mukherjee, L., Singh, V. (2014). Spectral Clustering with a Convex Regularizer on Millions of Images. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds) Computer Vision – ECCV 2014. ECCV 2014. Lecture Notes in Computer Science, vol 8691. Springer, Cham. https://doi.org/10.1007/978-3-319-10578-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-10578-9_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10577-2
Online ISBN: 978-3-319-10578-9
eBook Packages: Computer ScienceComputer Science (R0)