Entropy based statistical mechanical fuzzy clustering method and its visualization

研究了将确定性退火（DA）方法与模糊熵或Tsallis熵相结合的模糊聚类方法。在模糊c均值（FCM）方法的框架内，通过最大化模糊熵或Tsallis熵，得到类似于统计力学分布函数的隶属函数。从统计力学的角度研究了这些熵和隶属函数的特性。基于模糊熵和Tsallis熵的FCM都被表述为DA聚类。数值实验表明，与标准聚类方法相比，该算法能更准确、更稳定地划分数据。将快速退火（VFA）方法应用于数据处理中，确定温度的冷却计划。同时，隶属函数用线性函数逼近。计算结果表明，该方法可以缩短计算时间。多维问卷数据聚类，并通过省略一些维度，得到的聚类和隶属关系可视化。

The fuzzy clustering methods which combine the deterministic annealing (DA) approach with fuzzy entropy or Tsallis entropy are examined. By maximizing fuzzy entropy or Tsallis entropy within the framework of the fuzzy c-means (FCM) method, membership functions similar to the statistical mechanical distribution functions are obtained. The characteristics of these entropies and membership functions are investigated from the statistical mechanical point of view.Both fuzzy entropy and Tsallis entropy based FCM are formulated as DA clustering. Numerical experiments showed that these algorithms can divide data more properly and stably than the standard clustering method. The very fast annealing (VFA) method is applied to DA for cooling schedule of the temperature. Also, the membership functions are approximated by linear functions. The obtained results indicate that the proposed method can shorten computational times.Multidimensional questionnaire data were clustered and, by omitting some dimensions, the resultant clusters and memberships were visualized.