Probabilistic Principal Geodesic Deep Metric Learning

Dae Ha Kim,Byung Cheol Song

doi:10.1109/access.2022.3143129

Abstract

Similarity learning which is useful for the purpose of comparing various characteristics of images in the computer vision field has been often applied for deep metric learning (DML). Also, a lot of combinations of pairwise similarity metrics such as Euclidean distance and cosine similarity have been studied actively. However, such a local similarity-based approach can be rather a bottleneck for a retrieval task in which global characteristics of images must be considered important. Therefore, this paper proposes a new similarity metric structure that considers the local similarity as well as the global characteristic on the representation space, i.e., class variability. Also, based on an insight that better class variability analysis can be accomplished on the Stiefel (or Riemannian) manifold, manifold geometry is employed to generate class variability information. Finally, we show that the proposed method designed through in-depth analysis of generalization bound of DML outperforms conventional DML methods theoretically and experimentally.

Highlights

Deep metric learning (DML) is a learning method that can increase intra-class compactness and inter-class variability by quantifying intrinsic or extrinsic relationship between images
Since the existing DML methods [14], [37] are based on a similarity metric that can successfully encode the images of various attributes, they have been widely applied to product searching [32], face verification [37], perturbation analysis [30], etc
In order to overcome the drawbacks of the conventional DMLs, we come up with two ideas as follows: 1) Based on a pairwise similarity metric reflecting local characteristics, we reflect even a global characteristic in the representation space, i.e., class variability

Summary

INTRODUCTION

Deep metric learning (DML) is a learning method that can increase intra-class compactness and inter-class variability by quantifying intrinsic or extrinsic relationship between images. In order to overcome the drawbacks of the conventional DMLs, we come up with two ideas as follows: 1) Based on a pairwise similarity metric reflecting local characteristics, we reflect even a global characteristic in the representation space, i.e., class variability. Silhouette scores were highest in the order of Stiefel, Riemannian, and Euclidean space This result shows that compact representation in a matrix form enables discriminative class variability analysis. We derive class variability factor by using manifold sampling [55] and eigenpair obtained through DA in a nonlinear manifold such as Stiefel We map this factor into a one-dimensional line manifold to associate with a 1D similarity metric like Euclidean distance. We intend to design a GF that can reflect the spectrum of eigenpairs, i.e., global information on a nonlinear space

GEOMETRY OF MATRIX MANIFOLD

HYPER-PARAMETER SETTING

CONCLUSION AND FUTURE WORK

GENERALIZATION BOUND FOR GML-TRI

Findings

GENERALIZATION BOUND FOR GML-PA