Research On Low-Complexity Distance Metric Learning Algorithms

Distance metric learning(DML)serves as an important branch of machine learn-ing,Recent years has witnessed the rapid development of machine learning.Therefore,distance metric learning has received extensive attention and has been applied to var-ious real-world applications,such as image classification,image Retrieval,clustering,face recognition and pedestrian re-recognition,etc.Distance metric learning learns to obtain a robust distance metric by exploring the inherent statistical characteristics of the training data,and maps the data to a feature space in which similar samples gather together,and dissimilar samples are far away from each other,which helps to improve the performance of corresponding task.As a basic research direction,the progress of distance metric learning has promoted the development of various research fields.Traditional distance metric learning can directly obtain a Mahalanobis matrix or linear transformation,which is more intuitive and easier to add restrictions on the matrix and the linear transformation.However,the non-linearity requires kernel methods or other methods,which involves a lot of complexity mathematical derivations.With the development of deep convolutional neural networks(CNN)in recent years,the tradi-tional distance metric learning is combined with CNN,and deep metric learning comes into being.Deep metric learning integrates constraints into the loss function,and uses deep neural network as a nonlinear mapping function to learn a feature space.Thanks to the powerful learning ability of neural networks,generally speaking,the performance of deep metric learning is better than that of traditional distance metric learning.But deep metric learning requires relatively larger training data and computing resources to train the neural networks to achieve the desired goals.Therefore,the two methods have their advantages and disadvantages,which are worthy for our in-depth research,making rational use of their advantages while avoiding their shortcomings.With the development of computer and mobile phone applications,the amount of application data has increased amongyears.As people increased requirements for appli-cation performance and real-time performance,the demand for real-time applications,such as online applications is constantly increasing.How to improve the efficiency of distance metric learning and design a distance metric learning method with both low complexity and high-efficiency performance is very important.Therefore,the study of low-complexity distance metric learning methods is a research direction with far-reaching significance and bright future.This thesis focuses on the research of low-complexity distance metric learning al-gorithms with the hope that the performance of each task can be improved in a low-complexity manner.The existing traditional distance metric learning algorithms mainly directly learn a Mahalanobis matrix or learn a linear transformation.The existing deep metric learning algorithms can be roughly divided into three categories:learn-ing to fulfill instance-to-class similarity relationship constraints,learning according to the instance-to-proxy similarity relationship constraints,and learning to meet instance-to-instance similarity relationship constraints.These distance metric learning methods explore useful information in the training data,and have verified their performance in many tasks,but still have many shortcomings.(1)The complexity of directly learning Mahalanobis matrix or linear transformation is of the order of square.The complexity of algorithm is related to the dimensions of the input data,and it is difficult to extend to the case of high-dimensional data.(2)They cannot make full use of the information of the training data,introducing randomness in training or need to use training data from other domains for assistance.(3)The deep metric learning algorithms,which based on instance-to-class similarity constraints and instance-to-proxy similarity constraints,are often suffered from insufficient supervision information which leads to the degradation in performance.While the complexity of the algorithms based on instance-to-instance similarity constraints are at least squared which leads to low training efficiency and requires complex sampling and weighting mechanisms.(4)The current deep metric learning methods do not well explore the structural information of the data category,which is likely to cause the phenomenon of"supervision collapse".That is to say,the learned information is only conducive to improving the performance on the training set,and cannot be transferred well to the test set.This phenomenon is obvious in tasks such as person re-identification and fine-grained image retrieval,where the training set and test set have non-overlap categories.Focus on the above-mentioned problems,this paper designs low-complexity dis-tance metric learning methods to solve the shortcomings of existing algorithms.The work is mainly divided into three parts:semi-supervised coefficient-based distance metric learning,eigenvector-based distance metric learning,and guiding deep metric learning with prototypical distribution.First of all,semi-supervised coefficient-based distance metric learning aims at the problem that directly learning of Mahalanobis matrix or linear transformation suffer from high computation complexity.The semi-definite distance metric matrix is split into the linear combination of basis vectors,and the learning procedure can be conducted through learning linear combination coefficients of the basis vectors to approximate the target distance metric matrix,which reduce the variables and complexity from square to constant.In addition,a novel semi-supervised learning method is proposed to extend the algorithm to the semi-supervised learning framework,using potential information in unlabeled data.Aiming at the optimization of the non-smooth objective function,this paper proposes an optimization algorithm based on the alternating direction multi-plier method(ADMM),which directly obtains closed-form solution at each step and further improves the training speed and reduces the training cost.Especially,the pro-posed optimization algorithm accelerates the training process by nearly 30 times than the convex optimization(cvx)package on the face retrieval datasets.Semi-supervised coefficient-based distance metric learning use the random basis vectors which introduce randomness and cannot reflect the data information.Therefore,previous method learns the basis vectors using additional data from other domains which requires extra training data and resources.Eigenvector-based distance metric learning proposes to address these problems by introducing the explictly learned eigenvectors using training data.Most of the information can be obtained by only a few eigenvectors with the largest eigenvalues,which further improves the computational efficiency and the experimental performance,which has been verified on the large data sets of face retrieval.The current state-of-the-art deep metric learning algorithm relies on a large amount of pairwise similarity supervision information,and cannot explore the information of the data structure well,which may easily cause "supervision collapse" problem.To address these problems,"guide deep metric learning with prototypical distribution" proposes to use the prototype-level data structure as an additional supervision for deep metric learning,which reduces the dependence on the large amount of pairwise supervision information,and reduces the computational complexity from the square magnitude to the linear magnitude.On the other hand,the prototypical distribution proposed in this method can reflect the prototype-level data structure,enhancing the generalization abil-ity on the test set,and further improve the performance,which has been verified in person re-identification and fine-grained image retrieval tasks.