DEEP REPULSIVE CLUSTERING OF ORDERED DATA BASED ON ORDER-IDENTITY DECOMPOSITION

Abstract

We propose the deep repulsive clustering (DRC) algorithm of ordered data for effective order learning. First, we develop the order-identity decomposition (ORID) network to divide the information of an object instance into an order-related feature and an identity feature. Then, we group object instances into clusters according to their identity features using a repulsive term. Moreover, we estimate the rank of a test instance, by comparing it with references within the same cluster. Experimental results on facial age estimation, aesthetic score regression, and historical color image classification show that the proposed algorithm can cluster ordered data effectively and also yield excellent rank estimation performance.

1. INTRODUCTION

There are various types of 'ordered' data. For instance, in facial age estimation (Ricanek & Tesafaye, 2006) , face photos are ranked according to the ages. Also, in a video-sharing platform, videos can be sorted according to the numbers of views or likes. In these ordered data, classes, representing ranks or preferences, form an ordered set (Schröder, 2003) . Attempts have been made to estimate the classes of objects, including multi-class classification (Pan et al., 2018) , ordinal regression (Frank & Hall, 2001) , metric regression (Fu & Huang, 2008) . Recently, a new approach, called order learning (Lim et al., 2020) , was proposed to solve this problem. Order learning is based on the idea that it is easier to predict ordering relationship between objects than to estimate the absolute classes (or ranks); telling the older one between two people is easier than estimating their exact ages. Hence, in order learning, the pairwise ordering relationship is learned from training data. Then, the rank of a test object is estimated by comparing it with reference objects with known ranks. However, some objects cannot be easily compared. It is less easy to tell the older one between people of different genders than between those of the same gender. Lim et al. ( 2020) tried to deal with this issue, by dividing an ordered dataset into disjoint chains. But, the chains were not clearly separated, and no meaningful properties were discovered from the chains. In this paper, we propose a reliable clustering algorithm, called deep repulsive clustering (DRC), of ordered data based on order-identity decomposition (ORID). Figure 1 shows a clustering example of ordered data. Note that some characteristics of objects, such as genders or races in age estimation, are not related to their ranks, and the ranks of objects sharing such characteristics can be compared more reliably. To discover such characteristics without any supervision, the proposed ORID network decomposes the information of an object instance into an order-related feature and an identity feature unrelated to the rank. Then, the proposed DRC clusters object instances using their identity features; in each cluster, the instances share similar identity features. Furthermore, given a test instance, we decide its cluster based on the nearest neighbor (NN) rule, and compare it with reference instances within the cluster to estimate its rank. To this end, we develop a maximum a posteriori (MAP) estimation rule. Experimental results on ordered data for facial age estimation, aesthetic score regression (Kong et al., 2016) , and historical color image classification (Palermo et al., 2012) demonstrate that the proposed algorithm separates ordered data clearly into meaningful clusters and provides excellent rank estimation performances for unseen test instances. The contributions of this paper can be summarized as follows. 1

