Abstract
In recent years, linear representation-based methods have been widely researched and applied in the image classification field. Generally speaking, there are three steps within linear representation-based classification (LRC) algorithms. The first step is coding, which uses all training samples to represent the test sample in a linear combination. The second step is subspace approximation, where residuals between the test sample and the linear combination of each class are calculated. The third step is classification, which assigns the class label to the minimum class-specific residual. We classify the LRC methods into six categories: 1) linear representation-based classification methods with norm minimizations, 2) linear representation-based classification methods with constraints, 3) linear representation-based classification methods with feature spaces, 4) linear representation-based classification methods with structural information, 5) linear representation with subspace learning, and 6) linear representation in semi-supervised learning and unsupervised learning. The purpose of this paper is to: 1) make an accurate and clear definition of the linear representation-based method, 2) provide a categorization and a comprehensive survey of the existing linear representation-based classification methods for image classification, 3) Summarize the main applications of linear representation-based methods, 4) provide extensive classification results and a discussion of the linear representation-based methods. Furthermore, this paper summarizes specific applications of the linear representation-based methods. Particularly, we performed extensive experiments to compare thirteen linear representation-based classification methods on seven image classification datasets.
Highlights
I MAGE classification is a hot topic that has been extensively studied in recent years with the increasingly active developments of computer vision and pattern recognition
We reviewed the applications of linear representation-based classification (LRC) methods in the four most frequently used areas: remote sensing, face recognition, medical biometrics, and multimodal biometrics
2) Results that the optimal parameters have been selected for the LRC methods, we show its recognition rates on 7 datasets with an increasing number of training samples
Summary
I MAGE classification is a hot topic that has been extensively studied in recent years with the increasingly active developments of computer vision and pattern recognition. The linear representation-based classification method is an active research area in the image classification field [9]–[11]. To the best of our knowledge, there is no related literature that provides a clear definition of the linear representation-based method. We first make an accurate and clear definition of a linear representationbased method to establish the concept. Based on the definition, we proposed six categories to summarize various linear representation-based method into different perspectives to present both an overview and detailed interpretation. Afterwards, the main applications that widely apply linear representation-based methods were established. An accurate definition of linear representation-based classification will be provided and discussed. H represents the number of training samples in the task. is the operator performing element-wise product between two vectors
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