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The estimation of the gradient of a density function, with applications in pattern recognition
Abstract
Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in ak-nearest-neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.
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“Mean-shift clustering [37] is a nonparametric clustering technique that does not require prior knowledge of the number of clusters or constraints on cluster shape.”
From Machine learning: Algorithms, real-world applications and research directions (2021) · cites this paper as [37]
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Cited by
Machine learning: Algorithms, real-world applications and research directions
Sarker, I. H. (2021) · SN Computer Science · doi:10.1007/s42979-021-00592-x · Cited by 5,583
Clustering by fast search and find of density peaks
Rodriguez, A., & Laio, A. (2014) · Science · doi:10.1126/science.1242072 · Cited by 4,942
Hierarchical Density Estimates for Data Clustering, Visualization, and Outlier Detection
Campello, R. J. G. B., Moulavi, D., Zimek, A., & Sander, J. (2015) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/2733381 · Cited by 915
Deformable Model Fitting by Regularized Landmark Mean-Shift
Saragih, J. M., Lucey, S., & Cohn, J. F. (2011) · International Journal of Computer Vision · doi:10.1007/s11263-010-0380-4 · Cited by 787
Peng, H., Ruan, Z., Long, F., Simpson, J. H., & Myers, E. W. (2010) · Nature Biotechnology · doi:10.1038/nbt.1612 · Cited by 707
White, B. J., Berg, D. J., Kan, J. Y., Marino, R. A., Itti, L., & Munoz, D. P. (2017) · Nature Communications · doi:10.1038/ncomms14263 · Cited by 191
Generalized Density-Functional Tight-Binding Repulsive Potentials from Unsupervised Machine Learning
Kranz, J. J., Kubillus, M., Ramakrishnan, R., von Lilienfeld, O. A., & Elstner, M. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00933 · Cited by 63
Bottger, J., Schafer, A., Lohmann, G., Villringer, A., & Margulies, D. S. (2014) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2013.114 · Cited by 59
Romoa: Robust Model Aggregation for the Resistance of Federated Learning to Model Poisoning Attacks
Mao, Y., Yuan, X., Zhao, X., & Zhong, S. (2021) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-88418-5_23 · Cited by 48
Automated Rock Detection and Shape Analysis from Mars Rover Imagery and 3D Point Cloud Data
Di, K., Yue, Z., Liu, Z., & Wang, S. (2013) · Journal of Earth Science · doi:10.1007/s12583-013-0316-3 · Cited by 42
Exploring AI-Generated Text in Student Writing: How Does AI Help?
Woo, D. J., Susanto, H., Yeung, C. H., Guo, K., & Fung, A. K. Y. (2023) · arXiv · doi:10.48550/arxiv.2304.02478 · Cited by 39
Metadata
- Authors
- Fukunaga, K., & Hostetler, L.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1975-01
- Volume
- 21
- Issue
- 1
- Pages
- 32-40
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2164500538
- Cited by
- 3,043
- References
- 0
- FWCI
- 3.54
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
