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Because of its positive effects on dealing with the curse of dimensionality in big data, random projection for dimensionality reduction has become a popular method recently. In this paper, an academic analysis of influences of random projection on the variability of data set and the dependence of dimensions has been proposed. Together with the theoretical analysis, a new fuzzy c-means (FCM) clustering algorithm with random projection has been presented. Empirical results verify that the new algorithm not only preserves the accuracy of original FCM clustering, but also is more efficient than original clustering and clustering with singular value decomposition. At the same time, a new cluster ensemble approach based on FCM clustering with random projection is also proposed. The new aggregation method can efficiently compute the spectral embedding of data with cluster centers based representation which scales linearly with data size. Experimental results reveal the efficiency, effectiveness, and robustness of our algorithm compared to the state-of-the-art methods

mathematical problems in engineering

Fuzzy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:math>-Means and Cluster Ensemble with Random Projection for Big Data Clustering

Fuzzyc-Means and Cluster Ensemble with Random Projection for Big Data Clustering