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Unpublished Research

Outlier Detection Using Parzen Window
This was a final semester project during my final educational degree stint as a student in India. The goal was to detect outliers for very high dimensional data statistically using dimensionality reduction. For example if the data were to be obtained from a few classes, could we devise a very fast method for such data?
Fig. 1: Partially Parametric Statistical Outlier Detection
Figure 1 shows seven 2-dimensional independent and identical uniform distributions with one as an outlying class.

Original Image and selected corners

Crnr ID

"Canny" Edge Detec -tion

Detect -ed Corn -ers Crnr ID. "Canny" Edge Detect -ion Detect -ed Corn -ers

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It then gradually merges to the least number of clusters, c, using a fuzzy similarity function, that minimize the sum of squared distances of the data points to their respective cluster centers. The cluster merging was based on thresholding the similarity at a predetermined value much like hierarchical clustering.
Minimizing the within-cluster sum of squares of the data points does not always yield correct clusters using metrics like euclidean distances e.g. Mahalanobis distance e.g., this algorithm partitions a concentric ring data set (a main data set following a uniform circular distribution flanked by outlying data points generated from another uniform circular distribution) by a linear hyperplane. The output from the Matlab implementation of the algorithm is saved as an avi file.

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Fig 2: DIET corner detection - Corner detection using information theory
The middle one shows an example of the non-parameteric density estimation of the Mahalanobis distances from the median of the weighted data, the weights being the Tuckey's bi-weights. The third figure on the right shows a subset of the data at the tail of the density curve.

The full report titled "Statistical Outlier Detection in Large Multivariate Datasets" can be found here

Corner Detection in grayscale images using information theory

Another experimentation where we were tinkering with corner detection in gray scale images using Shannon's entropy.
The figure below only shows "some" detected corners and their corresponding zoomed-in image regions. See Figure 2 and the corresponding paper.

Outlier Detection using Fuzzy Clustering

Given a training data set comprising of p-featured overlapping and outlying data points, how can the outlying samples be identified while simultaneous clustering of the data using soft computing methods. The algorithm will run offline to obtain the value of the cut-off distance for online identification of outlying sample points.

We implemented an algorithm using fuzzy c-means that starts clustering with an arbitrary but given number of clusters, C.

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