Parzen Windows

Parzen windows are very similar to kNN. Both methods can generate very complex decision boundaries. The main difference is that instead of looking at the k closest points to a piece of training data, all points within a fixed distance are considered.

In practice, one difference is that datasets with large gaps get treated much different. kNN will pick far away points, but it is possible that relatively small Parzen Windows will actually enclose zero points. In this case, only the priors can be used to classify. Unfortunately, this dataset had many holes in it at the fringes, as was visible in the PDF graphs seen earlier.

I classified points using a variety of window sizes. I picked 20 equal-sized steps from the mininum to the maximum values of distGrid, the matrix which stores the distances from all points in the training set to all points in the testing set.

Feat. #	fwd	Bwd	rand
1	1	1	0
2	0	1	0
3	1	1	0
4	0	0	0
5	0	1	0
6	0	0	1
7	0	1	0
8	0	0	0
9	0	0	1
10	0	0	1
11	1	0	1
12	0	0	0
13	0	0	0
14	0	0	0
15	0	0	1
16	0	0	0
17	1	0	0
18	0	0	1
19	1	0	0
20	1	0	0
21	1	0	0
22	1	0	0
23	1	0	0
24	0	0	0
Validation Rate	62.02%	62.79%	58.91%
Testing Rate	58.8%	59.6%	58.1%

This method, too, might have been improved with a better window function.

--->Markov Model

Index