Document Type


Date of Award


Degree Name

Master of Science in Mechanical Engineering - (M.S.)


Mechanical and Industrial Engineering

First Advisor

Rajesh N. Dave

Second Advisor

Anthony D. Rosato

Third Advisor

Ian Sanford Fischer


In objective functional based fuzzy clustering algorithms the weighted sum of the distances of the feature vectors from cluster prototype are minimized. The fuzzy memberships are utilized as weighing factors. The cluster prototype can be a point or a line or a plane, etc. This work extends the recent concept of using curved prototypes by utilizing the Adaptive Norm Theorem proposed by Dave1 to develop an algorithm for the detection of fuzzy hyper-ellipsoidal shell prototypes. The Objective functional associates a norm for each cluster in which to measure the proximity of the shell prototype adaptively. The resulting implementation necessitates solving a set of non-linear equations through the application of the Newton's method which requires good starting values as a pre-requisite for convergence. A robust initialization scheme is presented to obtain good starting values for the partition and the prototype. The kind of substructures encountered are isolated and categorized into two groups and appropriate strategies suggested. Two schemes are suggested for the initial partition and the spatial properties of the domain are used to generate starting values for the prototypes. An iterative algorithm is outlined to obtain the starting guesses for the Newton's method. The algorithm is coerced to find a good initial guess by the use of different prototypes at different phases during its operation. Examples typifying substructures commonly encountered are shown to demonstrate the combined results of the initialization and the subsequent application of the AFCS algorithm. The problem of validating the number of subsets present in the data and the evaluation of the resulting substructure is also addressed. The existing validity measures for fuzzy clustering are surveyed and are shown to be partition based. Three new measures specifically designed to validate the shell substructure are introduced. Several examples are included to demonstrate the superiority of the new measures over the existing measures.

1 R. N. Dave and K. J. Patel, FCES Clustering Algorithm and detection of ellipsoidal shapes, Proc. of the SPIE Conf. on Intelligent Robots and Computer Vision IX , Boston, pp. 320-333, Nov.



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