Abstract: Here we will discuss about the Privacy-preserving High-order Possibilistic c-Means Algorithm. Fuzzy C- Means is a Clustering method that allows each data point to belong to multiple clusters with varying degree is membership. PCM is one of the methods used for C-means Clustering process and image analysis. The Process find out the two types of Clustering's like normal PCM clustering and important is HOPCM like (High Order PCM) FOR Big data clustering. The HOPCM method based on Map Reduce for very large amounts of heterogeneous data. Finally, a privacy-preserving HOPCM algorithm (PPHOPCM) to protect the private data on cloud by applying the BGV encryption scheme to HOPCM. To tackle this problem, the paper proposes a high-order PCM algorithm (HOPCM) for big data clustering by optimizing the objective function in the tensor space. Clustering is designed to separate objects into several different groups according to special metrics, making the objects with similar features in the same group. Clustering techniques have been successfully applied to knowledge discovery and data engineering. With the increasing popularity of big data, big data clustering is attracting much attention from data engineers and researchers.
Keywords: Possibilistic c-means (PCM), HOPCM, Map Reduce, PPHOPCM,BGV schema.