Large Scale Local Online Similarity/Distance Learning Framework based on Passive/Aggressive

Similarity/Distance measures play a key role in many machine learning, pattern recognition, and data mining algorithms, which leads to the emergence of metric learning field. Many metric learning algorithms learn a global distance function from data that satisfy the constraints of the problem. However, in many real-world datasets that the discrimination power of features varies in the different regions of input space, a global metric is often unable to capture the complexity of the task. To address this challenge, local metric learning methods are proposed that learn multiple metrics across the different regions of input space. Some advantages of these methods are high flexibility and the ability to learn a nonlinear mapping but typically achieves at the expense of higher time requirement and overfitting problem. To overcome these challenges, this research presents an online multiple metric learning framework. Each metric in the proposed framework is composed of a global and a local component learned simultaneously. Adding a global component to a local metric efficiently reduce the problem of overfitting. The proposed framework is also scalable with both sample size and the dimension of input data. To the best of our knowledge, this is the first local online similarity/distance learning framework based on PA (Passive/Aggressive). In addition, for scalability with the dimension of input data, DRP (Dual Random Projection) is extended for local online learning in the present work. It enables our methods to be run efficiently on high-dimensional datasets, while maintains their predictive performance. The proposed framework provides a straightforward local extension to any global online similarity/distance learning algorithm based on PA

Low-Rank Robust Online Distance/Similarity Learning based on the Rescaled Hinge Loss

An important challenge in metric learning is scalability to both size and dimension of input data. Online metric learning algorithms are proposed to address this challenge. Existing methods are commonly based on (Passive Aggressive) PA approach. Hence, they can rapidly process large volumes of data with an adaptive learning rate. However, these algorithms are based on the Hinge loss and so are not robust against outliers and label noise. Also, existing online methods usually assume training triplets or pairwise constraints are exist in advance. However, many datasets in real-world applications are in the form of input data and their associated labels. We address these challenges by formulating the online Distance-Similarity learning problem with the robust Rescaled hinge loss function. The proposed model is rather general and can be applied to any PA-based online Distance-Similarity algorithm. Also, we develop an efficient robust one-pass triplet construction algorithm. Finally, to provide scalability in high dimensional DML environments, the low-rank version of the proposed methods is presented that not only reduces the computational cost significantly but also keeps the predictive performance of the learned metrics. Also, it provides a straightforward extension of our methods for deep Distance-Similarity learning. We conduct several experiments on datasets from various applications. The results confirm that the proposed methods significantly outperform state-of-the-art online DML methods in the presence of label noise and outliers by a large margin.Comment: An Online Distance-Similarity learning approach in noisy environmen