Graph regularized nonnegative sparse coding using incoherent dictionary for approximate nearest neighbor search

Dai

et al. 2020

Applied Sciences

Self Cite

Student grade prediction (SGP) is an important educational problem for designing personalized strategies of teaching and learning. Many studies adopt the technique of matrix factorization (MF). However, their methods often focus on the grade records regardless of the side information, such as backgrounds and relationships. To this end, in this paper, we propose a new MF method, called graph regularized robust matrix factorization (GRMF), based on the recent robust MF version. GRMF integrates two side graphs built on the side data of students and courses into the objective of robust low-rank MF. As a result, the learned features of students and courses can grasp more priors from educational situations to achieve higher grade prediction results. The resulting objective problem can be effectively optimized by the Majorization Minimization (MM) algorithm. In addition, GRMF not only can yield the specific features for the education domain but can also deal with the case of missing, noisy, and corruptive data. To verify our method, we test GRMF on two public data sets for rating prediction and image recovery. Finally, we apply GRMF to educational data from our university, which is composed of 1325 students and 832 courses. The extensive experimental results manifestly show that GRMF is robust to various data problem and achieves more effective features in comparison with other methods. Moreover, GRMF also delivers higher prediction accuracy than other methods on our educational data set. This technique can facilitate personalized teaching and learning in higher education.

Section: Side Information Graphmentioning

confidence: 99%

Graphs Regularized Robust Matrix Factorization and Its Application on Student Grade Prediction

Dai

et al. 2020

Applied Sciences

Self Cite

“…In the first step, Euclidean distance is often used to compute the pairwise similarity. The second step uses the feature-sign search algorithm [25] for sparse decomposition and the Lagrange dual algorithm [5], [8], [9], [21] for dictionary learning. However, this avenue of GSC has the following drawbacks.…”

Section: A Our Motivationsmentioning

confidence: 99%

“…As is shown, the neighborhood graph is sensitive to the illumination and leads to a less discriminative prior, while the LRR graph discovers the multiple subspace structures in a discriminative graph. Thus, it is believed that using the LRR graph for regularizing sparse coding could result in more discriminative features and obtain better performance on subsequent tasks, e.g., images retrieval [5], clustering and classification [28], [30].…”

Section: A Our Motivationsmentioning

confidence: 99%

“…Sparse coding technique produces parsimonious data representations with the learned high-level semantic features and attracts many studies in the past twenty years [2]. Sparsity-based method has thus been developed in a wide range of domains, including signal restoration [3], compressive sensing [4], image retrieval [5], dimensionality reduction [6], cancer subtype discovery [7], image clustering [1], [8] and classification [9]- [11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Integrated Sparse Coding With Graph Learning for Robust Data Representation

Liu

2020

IEEE Access

Self Cite

Sparse coding is a popular technique for achieving compact data representation and has been used in many applications. However, the instability issue often causes degeneration in practice and thus attracts a lot of studies. While the traditional graph sparse coding preserves the neighborhood structure of the data, this study integrates the low-rank representation(LRR) to fix the inconsistency of sparse coding by holding the subspace structures of the high-dimensional observations. The proposed method is dubbed low-rank graph regularized sparse coding (LogSC), which learns sparse codes and low-rank representations jointly rather than the traditional two-step approach. Since the two data representations share a dictionary matrix, the resulted sparse representation on this dictionary could be benefited from LRR. We solved the optimization problem of LogSC by using the linearized alternating direction method with adaptive penalty. Experimental results show the proposed method is discriminative in feature learning and robust to various noises. This work provides a one-step approach to integrating graph embedding in representation learning. INDEX TERMS Graph sparse coding, graph embedding, data structure preserving, robust data representation, image representation, one-step integrated graph sparse coding.

“…Based on the graphregularized method, L. Sha et al [35] further introduced Locally Linear Embedding function regularization into DLSC model to improve the performance of image clustering tasks. Y. Zhang et al [36] applied the graph-regularized DLSC algorithm to the problem of approximate nearest neighbor (ANN) retrieval. The RGP-DLSC algorithm proposed in this paper is also derived from the idea of graph-regularized method in those Euclidean DLSC algorithms.…”

Section: Related Workmentioning

confidence: 99%

Robust Dictionary Learning and Sparse Coding With Riemannian Geometry Preserving Method in Symmetric Matrices Inner Product Space

Zhu

2020

IEEE Access

Existing Dictionary Learning and Sparse Coding (DLSC) algorithms for Symmetric Positive Definite (SPD) matrices usually adopt Reproducing Kernel Hilbert Space as workspace to perform necessary linear operations. But those methods heavily rely on ideal kernel maps and they are lack of robustness when facing different SPD data, especially in the case of high-sparsity coding. Different from existing methods, we explore a new workspace called Symmetric Matrices Inner Product Space (SMIPS) for modeling robust DLSC of SPD matrices. SMIPS, which can be treated as the minimal linear expansion space of SPD manifold, is a linear space equipped with a pre-defined inner product so it supports linear operations. Modelling DLSC in SMIPS is more intuitive, and SPD data can preserve matrix form in SMIPS. Then, in this paper, a Riemannian Geometry Preserving (RGP) method based on graph-regularized is proposed to include the Riemannian geometric information of original SPD data, so that improves the discriminability of sparse codes, and a sparse coding algorithm is developed to acquire sparse codes of SPD matrices in SMIPS efficiently, which extend the feature-sign search to such matrix space. For dictionary learning, an overall learning strategy utilizing the closed form solution of RGP codes is proposed to speed up the iterative dictionary learning process. Experiments on several computer vision tasks show that our algorithm is more robust even with high-sparsity coding across different datasets and outperforms other comparative algorithms in terms of recognition accuracy and learning efficiency, which also demonstrates the validity of SMIPS as a workspace.