Feature reduction fuzzy C-Means algorithm leveraging the marginal kurtosis measure

The feature reduction fuzzy c-means (FRFCM) algorithm has been proven to be effective for clustering data with redundant/unimportant feature(s). However, the FRFCM algorithm still has the following disadvantages. 1) The FRFCM uses the mean-to-variance-ratio (MVR) index to measure the feature importance of a dataset, but this index is affected by data normalization, i.e., a large MVR value of original feature(s) may become small if the data are normalized, and vice versa. Moreover, the MVR value(s) of the important feature(s) of a dataset may not necessarily be large. 2) The feature weights obtained by the FRFCM are sensitive to the initial cluster centers and initial feature weights. 3) The FRFCM algorithm may be unable to assign the proper weights to the features of a dataset. Thus, in the feature reduction learning process, important features may be discarded, but unimportant features may be retained. These disadvantages can cause the FRFCM algorithm to discard important feature components. In addition, the threshold for the selection of the important feature(s) of the FRFCM may not be easy to determine. To mitigate the disadvantages of the FRFCM algorithm, we first devise a new index, named the marginal kurtosis measure (MKM), to measure the importance of each feature in a dataset. Then, a novel and robust feature reduction fuzzy c-means clustering algorithm called the FRFCM-MKM, which incorporates the marginal kurtosis measure into the FRFCM, is proposed. Furthermore, an accurate threshold is introduced to select important feature(s) and discard unimportant feature(s). Experiments on synthetic and real-world datasets demonstrate that the FRFCM-MKM is effective and efficient.