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Candid covariance-free incremental principal component analysis
Abstract
Appearance-based image analysis techniques require fast computation of principal components of high-dimensional image vectors. We introduce a fast incremental principal component analysis (IPCA) algorithm, called candid covariance-free IPCA (CCIPCA), used to compute the principal components of a sequence of samples incrementally without estimating the covariance matrix (so covariance-free). The new method is motivated by the concept of statistical efficiency (the estimate has the smallest variance given the observed data). To do this, it keeps the scale of observations and computes the mean of observations incrementally, which is an efficient estimate for some well known distributions (e.g., Gaussian), although the highest possible efficiency is not guaranteed in our case because of unknown sample distribution. The method is for real-time applications and, thus, it does not allow iterations. It converges very fast for high-dimensional image vectors. Some links between IPCA and the development of the cerebral cortex are also discussed.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Turk, M., & Pentland, A. (1991) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1991.3.1.71 · Cited by 13,733
Cited by
Greenacre, M., Groenen, P. J. F., Hastie, T., D’Enza, A. I., Markos, A., & Tuzhilina, E. (2022) · Nature Reviews Methods Primers · doi:10.1038/s43586-022-00184-w · Cited by 1,773
The hippocampus as a predictive map
Stachenfeld, K. L., Botvinick, M. M., & Gershman, S. J. (2017) · Nature Neuroscience · doi:10.1038/nn.4650 · Cited by 1,000
Incremental nonlinear dimensionality reduction by manifold learning
Law, M. H. C., & Jain, A. K. (2006) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2006.56 · Cited by 284
MgSvF: Multi-Grained Slow versus Fast Framework for Few-Shot Class-Incremental Learning
Zhao, H., Fu, Y., Kang, M., Tian, Q., Wu, F., & Li, X. (2024) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3133897 · Cited by 115
Lughofer, E., Pollak, R., Zavoianu, A.-C., Meyer-Heye, P., Zorrer, H., Eitzinger, C., Lehner, J., Radauer, T., & Pratama, M. (2018) · 2018 IEEE Conference on Evolving and Adaptive Intelligent Systems (EAIS) · doi:10.1109/eais.2018.8397186 · Cited by 4
Metadata
- Authors
- Weng, J., Zhang, Y., & Hwang, W.-S.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2003-08
- Volume
- 25
- Issue
- 8
- Pages
- 1034-1040
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2141681031
- Cited by
- 464
- References
- 2
- FWCI
- 15.32
- Type
- journal article
- Language
- en
- Open access
- closed
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- Weng, J., Zhang, Y., & Hwang, W.-S. (2003). Candid covariance-free incremental principal component analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/tpami.2003.1217609
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