13-07-2012, 12:36 PM
Unsupervised Optimal Fuzzy Clustering
Unsupervised Optimal Fuzzy .ppt (Size: 1.78 MB / Downloads: 39)
Fuzzy Sets and Membership Functions
You are approaching a red light and must advise a driving student when to apply the brakes. What would you say:
“Begin braking 74 feet from the crosswalk”?
“Apply the brakes pretty soon”?
Everyday language is one example of the ways vagueness is used and propagated.
Imprecision in data and information gathered from and about our environment is either statistical (e.g., the outcome of a coin toss is a matter of chance) or nonstatistical (e.g., “apply the brakes pretty soon”).
This latter type of uncertainty is called fuzziness.
Fuzzy Sets and Membership Functions
We all assimilate and use fuzzy data, vague rules, and imprecise information.
Accordingly, computational models of real systems should also be able to recognize, represent, manipulate, interpret, and use both fuzzy and statistical uncertainties.
Statistical models deal with random events and outcomes; fuzzy models attempt to capture and quantify nonrandom imprecision.
Fuzzy Sets and Membership Functions
Because the property “close to 7” is fuzzy, there is not a unique membership function for F. Rather, it is left to the modeler to decide, based on the potential application and properties desired for F, what mF® should be like.
The membership function is the basic idea in fuzzy set theory; its values measure degrees to which objects satisfy imprecisely defined properties.
Fuzzy memberships represent similarities of objects to imprecisely defined properties.
Membership values determine how much fuzziness a fuzzy set contains.
Difficulties with Fuzzy Clustering
The optimal number of clusters K to be created has to be determined (the number of clusters cannot always be defined a priori and a good cluster validity criterion has to be found).
The character and location of cluster prototypes (centers) is not necessarily known a priori, and initial guesses have to be made.
Objectives and Challenges
Create an algorithm for fuzzy clustering that partitions the data set into an optimal number of clusters.
This algorithm should account for variability in cluster shapes, cluster densities, and the number of data points in each of the subsets.
Cluster prototypes would be generated through a process of unsupervised learning.