The estimation of the gradient of a density function, with applications in pattern recognition
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 estimat...
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| Veröffentlicht in: | IEEE transactions on information theory 1975-01, Vol.21 (1), p.32-40 |
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| container_end_page | 40 |
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| container_issue | 1 |
| container_start_page | 32 |
| container_title | IEEE transactions on information theory |
| container_volume | 21 |
| creator | Fukunaga, K. Hostetler, L. |
| description | 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 a k -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. |
| doi_str_mv | 10.1109/TIT.1975.1055330 |
| format | Article |
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| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 1975-01, Vol.21 (1), p.32-40 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_ieee_primary_1055330 |
| source | IEEE Electronic Library (IEL) |
| subjects | Clustering algorithms Density functional theory Estimation Kernel Laboratories Pattern recognition Probability density function |
| title | The estimation of the gradient of a density function, with applications in pattern recognition |
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