density estimation

histogram: count sample number inside a region

K-nn: fix sample count $k$, volume $V$ varies

Parzen window: volume $V$ fixed, $k$ may vary

K-nn

fix sample count $k$ in a local region, volume $V$ varies:

1D example figure: nearest-K samples, the smaller radius gives greater probability

parzen window

window function, ( weight function, or can be a kernel function ) (TODO: kernel \& weight ??)

$k_n$ is the region sample count.

kernel function condition:

common kernels:

  1. sqare window
  2. gaussian kernel
  3. exponential window
  4. hypersphere kernel

proof of convergence:

$h_n$ selection (meanshift algorithm)