# Fuzzy Rough C-Mean Based Unsupervised CNN Clustering for Large-Scale Image Data
## 1 Introduction  
Image clustering [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13] is a consequential research field in image processing and computer vision applications. Nowadays, it has come into an age of big data (with many novel and portable digital devices). Every day millions of data are produced and worldwide a large number of digital images are uploaded to the cloud for storage or sharing. With more and more data being generated, efficiently consolidating the large-scale image data is becoming a demanding problem. However, many researchers focus on decreasing data from a large-scale dataset [14] and feature encoding [15] for large-scale image clustering. The reason for this is the existence of many redundant and noise samples among the entire large data [16]. Unsupervised clustering is an essential machine-learning technique that is utilized to discover the common natural cluster structure of an unlabeled dataset [17]. Therefore, a great clusteringalgorithm ought to depend as little as possible on earlier learning, which is typically not available before cluster analysis. Distinctive clustering techniques such as hierarchical clustering [18; 19; 20], centroid-based clustering [1; 22; 3; 4; 5; 21; 23], graph theoretical approaches [23; 24], and the density-based approach [25] have been broadly applied for image clustering. However, with the data quality increasing, another basic issue of data uncertainty unavoidably occurs: the big data themselves may contain a high measure of uncertainty, vagueness, and overlapping among clusters that is therefore a huge challenge to the clustering task. To overcome the above issues, two main mathematical tools of granular computing [26], rough set theory and fuzzy set theory, have been introduced into the clustering method to expose uncertainties among the raw data [27; 28; 29; 30; 31], which expand the clustering from hard-partition to soft-partition and in this manner shape an essential branch of the data clustering [32; 33; 34]. For example, Fuzzy C-Mean (FCM) clustering [35; 36], Rough C-Mean (RCM) clustering [37; 38], Hybrid Rough-Fuzzy clustering [27], and Fuzzy-Rough C-Mean (FRCM) clustering [39]. FCM is one prominent clustering algorithm generally utilized in the applied field by appointing a fuzzy membership to each sample and presenting a fuzziness weighting exponent. RCM describes a cluster by a center and pair of lower and upper approximations, which are weighed against diverse parameters in computing the new center in the algorithm. FRCM is the incorporation of rough set theory and fuzzy set theory in which each cluster is represented by a center, a crisp lower approximation and a fuzzy boundary in this algorithm, and the new center is a weighting average of the boundary and lower approximation. In our paper, we introduce FRCM-based unsupervised convolution neural network (CNN) clustering. A key component of our approach is the reliable noise-free samples that are selected by FRCM algorithm, during updating of cluster centers. The concept of fuzzy sets enables efficient handling of overlapping partitions and rough sets deal with the uncertainty of robust data. Deep learning (DL) has become a hot topic in the last couple of years. Deep learning is a developing and intense model that permits large-scale task-driven features to learn from big data. These improvements were obtained with supervised learning, whereas our goal is unsupervised image data clustering. A lot of remarkable deep-learning-based architectures have been proposed recently, such as the Deep Belief Network, Deep Boltzmann Machine, Deep Autoencoder, and Convolutional Neural Network (CNNs). However, the most well-known network architectures for image/video applications is CNN, including CNN based AlexNet [40], ResNet [41], VGG (Visual Geometry Group) [42], and FCN (Fully Convolutional Networks for semantic segmentation) [43]. Since they were introduced into deep learning, the CNNs have demonstrated a state-of-the-art accuracy in large-scale image classification.