THE FUZZY NEAREST PROTOTYPE CLASSIFIER

THE FUZZY NEAREST PROTOTYPE CLASSIFIER

Based on the fuzzy c-means method，the membership functionμi t=μi（xt）associated with the vector xt for the ith codebook is used

where n＞1 is the degree of fuzziness，andμit satisfies

For the sequence X，the fuzzy membershipμi（X）is defined as the following average membership

Using this definition，we obtain

Since the value ofμitincreases with decreasing the value of d（xt，i），therefore for the sequence X，a decision rule is stated as follows

select speaker i if

If there is no proper maximum，select the first speaker at which a common value is attained.

Note that from（9）and（11），μi（X）itself is a normalised score，therefore it can be used in speaker verification，where a claimed speaker i is accepted ifμi（X）is greater than a given threshold（Tran，1998a）.