# Adaptive Facial Imagery Clustering via Spectral Clustering and Reinforcement Learning
## 1 Introduction  
With the rapid development of computer vision and pattern recognition, face images, as one of the most common formats of visual information, provide a wide range of application prospects. Face images can be captured in many fields, including social media, forensic investigations, and surveillance monitoring, etc. [1, 2, 3]. However, these captured face images generally lack labels, which leads to difficulties in identifying them. The unknown identities (clusters) can range from a few dozen to thousands, and how to locate an efficient range or even an exact range raises an essential problem [4]. In addition, implementation of modern clustering algorithms [5, 6] is required to ensure the number of clusters as well as some adjustable parameters in advance. Therefore, it is important to design an efficient facial imagery clustering algorithm for image labeling. Recently, face image clustering has attracted a lot of interest from researchers [7, 8, 9, 10, 11]. [PERSON] et al. [7] presented a clustering method based on a spectral clustering and self-organizing feature mapping (SOM) neural network. [PERSON] et al. [8] proposed a deep face clustering method based on a residual graph convolutional network (RGCN). [PERSON] et al. [9] proposed a TV media mining system based on a DCNN to rapidly identify a specific individual in real-time processing video data. [PERSON] et al. [10] proposed a multiple segmentation technique combined with constrained spectral clustering to label facial images containing objects with complicated boundaries. [PERSON] et al. [11] proposed an approximate rank-order clustering algorithm for large-scale face image clustering. Despite the tremendous efforts that have been devoted to image clustering, most previous studies have not adapted to the illuminance, pose, and complicated background of images. In addition, existing studies have failed to estimate the number of clusters and the values of adjustable parameters. In general, face clustering involves face representation and a clustering model. Face representation is generally a numeric vector descriptor of a face image. In the literature [12; 13; 14; 15], most traditional hand-crafted face representations often lack robustness with respect to adverse factors within the imagery. The quality of the captured images is low due to the factors of illuminance, pose, and complicated background, etc. [PERSON] et al. [16] presented a fuzzy geometrical approach based on unit hypercubes for image contrast enhancement to solve this problem. [PERSON] et al. [17] learned the discriminative target feature by aligning the feature domain globally, while distinguishing the target clusters locally. Their method reduced the impact of illuminance, pose, and image quality. We adopt the significant progress that has been achieved in unconstrained face representation [18; 19; 20], which can alleviate the influence of underlying factors by using a convolutional neural network-based face representation. Spectral clustering is an example of graph-based clustering algorithms. As compared with other clustering algorithms such as hierarchical clustering methods and K-means, spectral clustering has more robustness with respect to the uncertainty of data sparsity and distribution. Therefore, we use spectral clustering as the partition model. The main aim of this study is to propose an adaptive facial imagery clustering method, which mainly involves face representations, a spectral clustering model, and reinforcement learning (i.e., Q-learning used in this study) [21]. With Q-learning, the clustering model can adaptively search and find the optimal setting for the number of clusters and dimension reduction (i.e., the core adjustable parameter) in the spectral clustering model, which helps to dramatically improve the performance of clustering.