I have been learning the fuzzy clstering algorithm recently,and I got an object function as following:

\begin{array}{l} \min \;\;J = \sum\limits_{i = 1}^N {\sum\limits_{k = 1}^K {\sum\limits_{j = 1}^N {{u_{ik}}{d_{ij}}{u_{jk}}} + T\sum\limits_{i = 1}^N {\sum\limits_{k = 1}^K {u_{ik}^2} } } } \\ \text{s.t. }\;\;\sum\limits_{k = 1}^K {{u_{ik}}} = 1,\;\;{u_{ik}} \ge 0\\\\ N: \text{ number of samples}\\ K: \text{ number of clusters}\\ {u_{ik}}: \text{ the fuzzy membership, which represents that the degree of object } i\\\qquad\,\text{ belongs to cluster }k\\ {d_{ij}}: \text{the distance of object $i$ and object }j\;\\ T: \text{ parameter,a constant} \end{array}

I am interested in this algorithm but I have no idea what is the name or meaning of it.The only thing I know about it is that it`s a fuzzy clustering algorithm. It looks like an variant of the fuzzy c-means clustering algorithm and K-medoids?

What I have already known is the meaning of the first item in the formula is the total dissimilarity within each cluster.However,I can not figure out the reason of it...

I searched via the Internet however I can`t find anything looks like this formula.I will appreciate it if you could help me or give me a hint.

I asked this question on(https://math.stackexchange.com/questions/2968881/whats-the-name-of-this-clustering-algorithm?noredirect=1#comment6128593_2968881),@Nitin advised me to ask here,thank him!


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