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The Partition Based Solution

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Reference

Interactive Applet

Instructions:

There are 3 modes of this applet:

1. Edit Mode: Initially the applet is in Edit Mode. You may get back to this mode any time by clicking on 'Edit Points' checkbox at the bottom.

  What you can do in Edit Mode:

   i) Add points: Click on the screen in the applet to add a new point. The points are marked in blue.

   ii) Generate uniformly distributed random points: By Clicking the Uniform Dist button, you'll be able to generate 20 uniformly distributed random points.

   iii) Generate normally distributed random points: By Clicking the Normal Dist button, you'll be able to generate 20 normally (gaussian) distributed random points.

   iv) Reset Points: Anytime you may reset points by clicking the Reset Points button.

    v) Increase/ Decrease Number of Nearest Neighbor to search: Click on the +/- button following the label Number of Nearest neighbor(k) to increase/ decrease the value of k.

    vi) Increase/ Decrease Number of Outliers to search: Click on the +/- button following the label Number of Outliers(n) to increase/ decrease the value of n.

2. Nearest Neighbor Mode: You may switch to this mode by clicking on 'Find Nearest Neighbor' checkbox at the bottom.

  What you can do in Nearest Neighbor Mode:

      i) Finding Nearest Neighbor: Click on any part of the screen, and the program will compute the number of nearest neighbors as you have specified as the value of k. The query point is marked in red, all the neighbors are marked in green. The radius of the black circle denotes the distance between the query point and k-th Nearest neighbor (D^k(query point)). 

      ii) Increase/ Decrease Number of Nearest Neighbor to search: Click on the +/- button following the label Number of Nearest neighbor(k) to increase/ decrease the value of k.

3. Outlier Mode: You may switch to this mode by clicking on 'Find Outliers' checkbox at the bottom.

  What you can do in Outlier Mode:

        i) Finding Outliers: As soon as you switch to outlier mode, the program will calculate the numbers of outliers as you have specified as the value of n. It will mark this outliers in red. It will draw a circle in green whose radius denote the distance between an outlier point and k-th Nearest neighbor of the outlier(D^k(outlier)).

      ii) Increase/ Decrease Number of Nearest Neighbor to search: Click on the +/- button following the label Number of Nearest neighbor(k) to increase/ decrease the value of k.

      iii) Increase/ Decrease Number of Outliers to search: Click on the +/- button following the label Number of Outliers(n) to increase/ decrease the value of n.

Explore the applet to get a feel of how the k-th Nearest Neighbor distance based formulation of outliers work.