Classification from Triplet Comparison Data

Abstract

Learning from triplet comparison data has been extensively studied in the context of metric learning, where we want to learn a distance metric between two instances, and ordinal embedding, where we want to learn an embedding in an Euclidean space of the given instances that preserves the comparison order as well as possible. Unlike fullylabeled data, triplet comparison data can be collected in a more accurate and humanfriendly way. Although learning from triplet comparison data has been considered in many applications, an important fundamental question of whether we can learn a classifier only from triplet comparison data has remained unanswered. In this paper, we give a positive answer to this important question by proposing an unbiased estimator for the classification risk under the empirical risk minimization framework. Since the proposed method is based on the empirical risk minimization framework, it inherently has the advantage that any surrogate loss function and any model, including neural networks, can be easily applied. Furthermore, we theoretically establish an estimation error bound for the proposed empirical risk minimizer. Finally, we provide experimental results to show that our method empirically works well and outperforms various baseline methods.

Three-Dimensional Aerodynamic Optimization of Turbine Blade Profile Considering Heat Transfer Performance

“…This assumption was commonly used in previous studies (Carbonneau et al, 2018;Cui et al, 2020;Zhang et al, 2020;Bao et al, 2022). It can be implied in the data collection process, e.g., when we first collect px, yq-pairs but Classification from ¨¨¨Size m Aggregate Information Aggregate Function g pairwise similarity m " 2 if y 1 and y 2 belong to same class or not gpy 1 , y 2 q " Iry 1 " y 2 s triplet comparison m " 3 if dpy 1 , y 2 q is smaller than dpy 1 , y 3 q gpy 1:3 q " Irdpy 1 , y 2 q ă dpy 1 , y3qs multiple instances m ě 2 if at least one positive label exits in y 1:m (k " 2) gpy 1:m q " maxpy 1:m q label proportion m ě 2 proportion of data from each class in the group g j py 1:m q " p ř m i"1 Iry i " jsq{m ordinal rank m " 2 if y 1 is larger than y 2 , i.e., y 1 ě y 2 .…”

“…Bao et al (2018a) stud-ied classification from pairwise similarities, where the aggregate information is whether two instances in the group belong to the same class (similar) or not (dissimilar). Cui et al (2020) studied classification from triplet comparisons, where the aggregate information is whether one instance is more similar to the other one, compared with the third one.…”

Comparing Class-Aware and Pairwise Loss Functions for Deep Metric Learning in Wildlife Re-Identification

“…Schroff et al [ 29 ] discussed the successes of similarity learning in the re-identification of human beings using facial images. There are a significant number of loss functions adopted in experiments for training similarity learning models, namely contrastive loss, triplet loss, and Proxy-NCA [ 30 , 31 , 32 ].…”

Pointwise Binary Classification with Pairwise Confidence Comparisons

“…Therefore, unlike some studies [19,31] that assume the positive confidence is known, we only assume that the labeling system has access to the full labels. Specifically, we adopt the assumption [23] that weakly supervised examples are first sampled from the true data distribution, but the labels are only accessible by the labeling system, not us. Then, the labeling system would provide us weakly supervised information (i.e., pairwise comparison information) according to the received labels.…”

“…In many real-world scenarios, it may be too difficult to collect such data. To alleviate this issue, a large number of weakly supervised learning problems [1] have been extensively studied, including semi-supervised learning [2,3,4], multi-instance learning [5,6,7], noisy-label learning [8,9,10], partiallabel learning [11,12,13], complementary-label learning [14,15,16,17], positive-unlabeled classification [18], positive-confidence classification [19], similar-unlabeled classification [20], unlabeled-unlabeled classification [21,22], and triplet classification [23].…”