# Difference between revisions of "proposal Fall 2010"

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− | In LDA, we assign a new data point to the class having the least distance to the center. At the same time however, it is desirable to assign a new data point to a class so that it is less of an outlier in that class as compared to every other class. To this end, compared to every other class, a new data point should be closer to the center of its assigned class and at the same time also be closer to | + | In LDA, we assign a new data point to the class having the least distance to the center. At the same time however, it is desirable to assign a new data point to a class so that it is less of an outlier in that class as compared to every other class. To this end, compared to every other class, a new data point should be closer to the center of its assigned class and at the same time also, after suitable weighting has been done, be closer to the directions of variation of its assigned class. |

− | Suppose there are two classes 0 and 1, and a new data point is given. To assign the new data point to a class, we can proceed using the following steps: | + | Suppose there are two classes 0 and 1 both having <math>\,d</math> dimensions, and a new data point is given. To assign the new data point to a class, we can proceed using the following steps: |

− | Step 1: | + | :::Step 1: For each class, find its center and its <math>\,d</math> directions of variation. |

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− | Step | + | :::Step 2: For the new data point, with regard to each of the two classes, sum up its distance to the center and its distance to each :::direction of variation weighted (multiplied) by the ratio of the amount of variation in that direction to the total variation. |

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− | ::: | + | :::Step 3: Assign the new point to the class having the smaller of these two sums. |

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## Revision as of 12:16, 24 October 2010

## Project 1 : Classifying New Data Points Using An Outlier Approach

### By: Yongpeng Sun

Intuition:

In LDA, we assign a new data point to the class having the least distance to the center. At the same time however, it is desirable to assign a new data point to a class so that it is less of an outlier in that class as compared to every other class. To this end, compared to every other class, a new data point should be closer to the center of its assigned class and at the same time also, after suitable weighting has been done, be closer to the directions of variation of its assigned class.

Suppose there are two classes 0 and 1 both having [math]\,d[/math] dimensions, and a new data point is given. To assign the new data point to a class, we can proceed using the following steps:

- Step 1: For each class, find its center and its [math]\,d[/math] directions of variation.

- Step 2: For the new data point, with regard to each of the two classes, sum up its distance to the center and its distance to each :::direction of variation weighted (multiplied) by the ratio of the amount of variation in that direction to the total variation.

- Step 3: Assign the new point to the class having the smaller of these two sums.

These 3 steps can be easily generalized to the case where the number of classes is more than 2 because, to assign a
new data point to a class, we only need to know, with regard to each class, the sum as described above.

I would like to evaluate the effectiveness of my idea / algorithm as compared to LDA and QDA and other classifiers using data sets in the UCI database ( http://archive.ics.uci.edu/ml/ ).