L6 - be empty General Formulation • Assume observations...

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EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 6: Nonparametric Density Estimation
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Nonparametric density estimation Parametric distribution models are restricted to specific forms, which may not always be suitable. Nonparametric approaches do not make any parametric assumptions about the distribution of data.
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The Histogram The histogram method partitions the sample space into a number of distinct bins, estimates the pdf at x as the fraction of the training samples in the same bin: Total number of samples
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The Histogram The bin width acts as a smoothing parameter. Too smooth Too “spiky” Drawbacks of the histogram method: The density estimate depends on bin locations. There are discontinuities at bin boundaries. The number of bins grow exponentially with the number of dimensions. In high dimensions, a lot of samples are required, otherwise, most bins would
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Unformatted text preview: be empty. General Formulation • Assume observations are drawn from a density p(x) and consider a small region R containing x. Let V be the volume of R. Nonparametric Estimation When applying this result to practical density estimation problems, two basic approaches can be adopted: • We can choose a fixed value of the volume V, and determine k from the data. This is referred as Kernel Density Estimation (KDE). • We can choose a fixed value of k, and determine the corresponding volume V from the data. This approach is known as k Nearest Neighbor (kNN) approach. Parzen window Parzen window Parzen window Parzen window x Parzen window - Example Smooth Kernels hypercube Smooth Kernels Choosing the bandwidth Number of samples and bandwidth Bandwidth and Decision Regions Small bandwidth Large bandwidth Example...
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This note was uploaded on 09/21/2010 for the course EE EE7750 taught by Professor Bahadirgunturk during the Fall '10 term at LSU.

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L6 - be empty General Formulation • Assume observations...

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