Fuzzy Clustering of Single-View Incomplete Data Using a Multiview Framework
Suvra Jyoti Choudhury, Nikhil Ranjan Pal · IEEE Transactions on Fuzzy Systems · 2022
We propose four frameworks for clustering data with missing values. We first use a very simple method to impute the missing values and generate multiple imputed versions of the data. These views are then clustered together to obtain a common partition matrix and a common set of centroids. As the clustering framework, we use a multiview version of the Fuzzy-c-Means (MVFCM) and a multiview version of Kernelized Fuzzy-c-Means (MVKFCM). To find the importance (weights) of different views, we use an entropic regularization term using the weights. After obtaining the optimal weights, the final imputation is done as a weighted sum (convex combination) of the imputed values used to generate the views. The final clustering is done on this imputed data set. We compare the performance of the proposed algorithms with several algorithms using Normalized Mutual Information, Adjusted Rand Index, and cluster accuracy on 12 benchmark data sets. Of these algorithms, the MVKFCM is found to perform the best. The MVFCM and MVKFCM use$5 \times r$views, where$r$is the number of classes (note that the class labels are not used). However,$r$may not be known, and also for large$r$, there will be too many views. So we propose two variants of MVKFCM:$MVKFCM_{FV}$and$MVKFCM_{RFV}$(FVstands for a fixed number of views andRFVstands for a robust version with fixed views). The$MVKFCM_{RFV}$generates views in a manner that helps to obtain robust performance. As expected,$MVKFCM_{RFV}$is found to be the best performing algorithm.