COS-LDL: Label Distribution Learning by Cosine-Based Distance-Mapping Correlation

Abstract

Label distribution learning (LDL) is a popular research trend in multi-label learning. Competing methods have been designed to improve the predictive performance. In this paper, we propose a method called cosine-based correlation for LDL (COS-LDL). The key issue is how to exploit correlations among different labels of the same instance. We propose a distance-mapping function for this purpose. With this mapping function, we design an objective function and its corresponding learning algorithm. Experiments undertaken on thirteen real-world datasets compare with eight LDL state-of-the-art methods. Results demonstrate that COS-LDL outperforms them in eight out of ten popular measures. INDEX TERMS Cosine similarity, distance-mapping matrix, label correlation, label distribution learning. I. INTRODUCTION Label distribution learning (LDL) [1]-[6] is a generalization of multi-label learning (MLL) [7]-[13]. It was first presented by Geng [3]. Unlike traditional MLL, which outputs a label set, LDL outputs a label distribution. MLL handles the ambiguity of ''what describes the instance.'' In contrast, LDL [3] deals with the more general ambiguity of ''how to describe the instance.'' Figure 1(a) is an image of the sea [14]. Figure 1(b) shows the labels city and sea obtained by MLL, and Fig. 1(c) shows the distribution of the four labels obtained by LDL. Naturally, LDL provides richer information than does MLL. LDL methods are gaining increasing attention in areas such as soft video parsing [15], age estimation [16]-[19], and crowd counting [20]. Various LDL methods have been designed to improve the predictive performance [3], [21], [22]. Geng [3] proposed the IIS-LLD method by transforming the single-label data into distribution data. This method does not consider the correlations among the labels. Jia et al. [21] introduced Pearson's correlation coefficients to describe label correlations. The associate editor coordinating the review of this manuscript and approving it for publication was Juan Wang .

In-Depth Research and Analysis of Multilabel Learning Algorithm

“…A literature confirmed that the optimize process of IIS-LLD algorithm was ineffective. SA-BFGS improved the aforementioned optimization process by BFGS Quasi-Newton method [38]. SA-BFGS expanded formula (43) into second-order Taylor expansion at θ ðlÞ of l th round, obtaining…”

Label distribution learning with high‐order label correlations

“…9 Zhang et al adopted a cosine distance map to measure label correlations. 10 Although the above studies considered label correlations, most of them only measure the correlation of label pairs. Such second-order strategy may not reflect the complex high-order relationships between labels.…”

“…Ren et al obtained label correlations through the low‐rank matrix constraint 9 . Zhang et al adopted a cosine distance map to measure label correlations 10 …”