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Fast and scalable polynomial kernels via explicit feature maps
Abstract
Approximation of non-linear kernels using random feature mapping has been successfully employed in large-scale data analysis applications, accelerating the training of kernel machines. While previous random feature mappings run in O(ndD) time for $n$ training samples in d-dimensional space and D random feature maps, we propose a novel randomized tensor product technique, called Tensor Sketching, for approximating any polynomial kernel in O(n(d+D \log{D})) time. Also, we introduce both absolute and relative error bounds for our approximation to guarantee the reliability of our estimation algorithm. Empirically, Tensor Sketching achieves higher accuracy and often runs orders of magnitude faster than the state-of-the-art approach for large-scale real-world datasets.
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Lecun, Y., Bottou, L., Bengio, Y., & Haffner, P. (1998) · Proceedings of the IEEE · doi:10.1109/5.726791 · Cited by 58,805
LIBSVM: A library for support vector machines
Chang, C.-C., & Lin, C.-J. (2011) · ACM Transactions on Intelligent Systems and Technology · doi:10.1145/1961189.1961199 · Cited by 40,918
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Guo, W., Wang, J., & Wang, S. (2019) · IEEE Access · doi:10.1109/access.2019.2916887 · Cited by 535
Multimodal intelligence: Representation learning, information fusion, and applications
Zhang, C., Yang, Z., He, X., & Deng, L. (2020) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2020.2987728 · Cited by 511
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Kong, S., & Fowlkes, C. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.743 · Cited by 367
Bilinear Convolutional Neural Networks for Fine-Grained Visual Recognition
Lin, T.-Y., RoyChowdhury, A., & Maji, S. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2723400 · Cited by 328
Metadata
- Authors
- Pham, N., & Pagh, R.
- Venue
- Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
- Publisher
- ACM
- Published
- 2013-08-11
- Pages
- 239-247
- OpenAlex
- W2146897752
- Cited by
- 306
- References
- 2
- FWCI
- 9.76
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Pham, N., & Pagh, R. (2013). Fast and scalable polynomial kernels via explicit feature maps. Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining. https://doi.org/10.1145/2487575.2487591
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