Abstract

Constructing a powerful graph that can effectively depict the intrinsic connection of data points is the critical step to make the graph-based semisupervised learning algorithms achieve promising performance. Among popular graph construction algorithms, low-rank representation (LRR) is a very competitive one that can simultaneously explore the global structure of data and recover the data from noisy environments. Therefore, the learned low-rank coefficient matrix in LRR can be used to construct the data affinity matrix. Consider the existing problems such as the following: (1) the essentially linear property of LRR makes it not appropriate to process the possible nonlinear structure of data and (2) learning performance can be greatly enhanced by exploring the structure information of data; we propose a new manifold kernelized low-rank representation (MKLRR) model that can perform LRR in the data manifold adaptive kernel space. Specifically, the manifold structure can be incorporated into the kernel space by using graph Laplacian and thus the underlying geometry of data is reflected by the wrapped kernel space. Experimental results of semisupervised image classification tasks show the effectiveness of MKLRR. For example, MKLRR can, respectively, obtain 96.13%, 98.09%, and 96.08% accuracies on ORL, Extended Yale B, and PIE data sets when given 5, 20, and 20 labeled face images per subject.

Highlights

  • Since it is usually not easy to collect a large number of labeled samples to train learning models, the semisupervised learning (SSL) paradigm, which can harness both labeled and unlabeled samples to improve the learning performance, draws a lot of attention in recent studies [1,2,3,4,5,6,7]

  • Consider the existing problems such as the following: (1) the essentially linear property of LRR makes it not appropriate to process the possible nonlinear structure of data and (2) learning performance can be greatly enhanced by exploring the structure information of data; we propose a new manifold kernelized low-rank representation (MKLRR) model that can perform LRR in the data manifold adaptive kernel space

  • Since sparse representation encodes each datum individually, the resultant sparse graph only emphasizes the local structure of data, while it neglects considering the global structure of data

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Summary

Introduction

Since it is usually not easy to collect a large number of labeled samples to train learning models, the semisupervised learning (SSL) paradigm, which can harness both labeled and unlabeled samples to improve the learning performance, draws a lot of attention in recent studies [1,2,3,4,5,6,7]. Since sparse representation encodes each datum individually, the resultant sparse graph only emphasizes the local structure of data, while it neglects considering the global structure of data. This property will deteriorate its performance, especially when data are grossly corrupted [13]. To make the low-rank model effectively deal with the nonlinear structure of data, [11] proposed the kernel low-rank representation (KLRR) graph for semisupervised classification by using kernel trick. We propose a novel manifold adaptive kernelized LRR for semisupervised classification.

Related Work
Manifold Adaptive Low-Rank Representation
Experiments
Findings
Conclusion and Future Work
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