# Flexible Metric NN Classification - PowerPoint PPT Presentation

1 / 13

Flexible Metric NN Classification. based on Friedman (1995) David Madigan. Nearest-Neighbor Methods. k -NN assigns an unknown object to the most common class of its k nearest neighbors Choice of k ? (bias-variance tradeoff again) Choice of metric?

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Flexible Metric NN Classification

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Flexible Metric NN Classification

based on Friedman (1995)

### Nearest-Neighbor Methods

• k-NN assigns an unknown object to the most common class of its k nearest neighbors

• Choice of k? (bias-variance tradeoff again)

• Choice of metric?

• Need all the training to be present to classify a new point (“lazy methods”)

• Surprisingly strong asymptotic results (e.g. no decision rule is more than twice as accurate as 1-NN)

### Suppose a Regression Surface Looks like this:

want this

not this

Flexible-metric NN Methods try to capture this idea…

### FMNN

• Predictors may not all be equally relevant for classifying a new object

• Furthermore, this differential relevance may depend on the location of the new object

• FMNN attempts to model this phenomenon

### Local Relevance

• Consider an arbitrary function f on Rp

• If no values of x are known, have:

• Suppose xi=z, then:

### Local Relevance cont.

• The improvement in squared error provided by knowing xi is:

• I2i(z) reflects the importance of the ith variable on the variation of f(x) at xi=z

### Local Relevance cont.

• Now consider an arbitrary point z=(z1,…,zp)

• The relative importance of xi to the variation of f at x=z is:

• R2i(z)=0 when f(x) is independent of xi at z

• R2i(z)=1 when f(x) depends only on xi at z

• Recall:

### On To Classification

• For J-class classification have {yj}, j=1,…,J output variables, yje {0,1}, S yj=1.

• Can compute:

• Technical point: need to weight the observations to rectify unequal variances

### The Machete

• Compute

• Then:

• Continue until Ri contains K points

M1th order statistic