# Fuzzy Rough C-Mean Based Unsupervised CNN Clustering for Large-Scale Image Data
## 1 Introduction
CNN based architectures play an important role in the processing of image data due to their unique structure in the phase of feature representation, given a sufficiently large labeled training set. The performance of clustering greatly depends on (1) noise reduction and (2) feature representational power. There have been few attempts to increase the performance of image clustering by deep-networks-based feature representation learning. Nevertheless, deep-networks-based feature representational learning does depend on much labeled training data, which is not accessible in unsupervised clustering. To overcome this problem, the model can be pre-trained in view of existing large-scale training image sets; the pre-trained model cannot fit the normal input data divider. Various works have investigated consolidating image clustering with representation learning [44; 45; 46; 47]. [PERSON] [44] proposed CNN-based joint clustering in which Mini-batch K-Mean is then executed to assign cluster labels. However, it is a completely deterministic model that sheds no light on data uncertainty reduction. [PERSON] [45] proposed Auto-Encoder based deep-learning, figuring out how to learn visual representations followed by conventional K-Mean to get the final cluster. However, for high-dimensional data, the Auto-Encoder generally cannot learn representative features appropriately. [PERSON] (CNN-CM) [46] and [PERSON] (CNN-RC) [47; 48] proposed CNN-based clustering with connection Matrix and re-running clustering respectively. However, when the size of the image data is large then it devours high computation and memory complexity. Instead, an unnecessary number of input data would increase the parameter fine-tuning frequency of CNNs; this could cause the risk of uncertainties and over-fitting among the raw data [49; 50]. Therefore, it is normal to reason that there must be considerable noise and redundant data in large-scale data sets. To overcome the above issues, the contribution of our work is that we can decrease the training time and furthermore maintain and even improve the test accuracy by selecting noise-free data for updating clusters by using the Fuzzy-Rough C-Mean (FRCM) algorithm. In this paper, we satisfy the model with unsupervised CNN clustering and FRCM algorithm. Our proposed clustering algorithm benefits from both CNNs and FRCM by merging one with the other; this is shown in Figure 1. Unsupervised CNN clustering (UCNN) architecture is proposed, which can extract salient features to produce the initial cluster centers. During the learning stage the cluster and representation are updating simultaneously: cluster centers are updating based on robust free samples by FRCM algorithm in forward-pass and the parameters of representation are updating in backward-pass on stochastic gradient descent (SGD). The main idea behind our method is that good representations are beneficial to image clustering and better clustering results beneficial for feature representations. The main contributions of the proposed algorithm are as follows:  
1. We present an FRCM-based unsupervised CNN clustering, which is robust to the uncertainties in the training data and could achieve reliable performances even with noisy samples. 2. We propose a joint learning framework to simultaneously update the parameter of unsupervised CNN and the cluster centroid iteratively. 3. We introduce FRCM with CNN to reduce the time complexity and increase cluster performance by updating the cluster centers based on a reliable sample selection, which is a key component of our method to ensure its success. 4. Extensive experiments on large-scale image datasets indicate that our strategy to enhance the clustering accuracy, when compared with other non-fuzzy deep neural networks, show that fuzzy learning is without a doubt a conceivable method to further improve the performance of deep-learning-based clustering algorithms.