Robust metric learning based on the rescaled hinge loss
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ORIGINAL ARTICLE
Robust metric learning based on the rescaled hinge loss Sumia Abdulhussien Razooqi Al‑Obaidi1 · Davood Zabihzadeh2 · Hamideh Hajiabadi3 Received: 14 June 2019 / Accepted: 2 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Distance/Similarity learning is a fundamental problem in machine learning. For example, kNN classifier or clustering methods are based on a distance/similarity measure. Metric learning algorithms enhance the efficiency of these methods by learning an optimal distance function from data. Most metric learning methods need training information in the form of pair or triplet sets. Nowadays, this training information often is obtained from the Internet via crowdsourcing methods. Therefore, this information may contain label noise or outliers leading to the poor performance of the learned metric. It is even possible that the learned metric functions perform worse than the general metrics such as Euclidean distance. To address this challenge, this paper presents a new robust metric learning method based on the Rescaled Hinge loss. This loss function is a general case of the popular Hinge loss and initially introduced in Xu et al. (Pattern Recogn 63:139–148, 2017) to develop a new robust SVM algorithm. In this paper, we formulate the metric learning problem using the Rescaled Hinge loss function and then develop an efficient algorithm based on HQ (Half-Quadratic) to solve the problem. Experimental results on a variety of both real and synthetic datasets confirm that our new robust algorithm considerably outperforms state-of-the-art metric learning methods in the presence of label noise and outliers. Keywords Metric learning · Rescaled hinge loss · Robust algorithm · Label noise · Outlier · Half quadratic (HQ) optimization
1 Introduction Similarity/Distance measures are a key component in many machine learning and data mining algorithms. For example, clustering methods or kNN classifier are based on a similarity/distance measure. In addition, information retrieval systems require a measure to sort the retrieved objects based on degrees of relevancy to a query object. However, standard measures such as Euclidean distance or cosine similarity are * Davood Zabihzadeh [email protected] Sumia Abdulhussien Razooqi Al‑Obaidi [email protected] Hamideh Hajiabadi [email protected] 1
Supervision and Scientific. Evaluation Apparatus, Ministry of Higher Education and Scientific Research, Baghdad, Iraq
2
Computer Department, Engineering Faculty, Sabzevar University of New Technology, Sabzevar, Iran
3
Department of Computer Engineering, Birjand University of Technology, Birjand, Iran
not appropriate for many applications. For example in Fig. 1, the w1 feature, unlike w2 , is useful to discriminate data for the classification task while standard measures assign the same weight to both of these features. Metric learning learns a distance function from data which brings conceptually related data items together while keeps unrelated
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