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NRIC: A Noise Removal Approach for Nonlinear Isomap Method

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Abstract

Nonlinear manifold learning is a popular dimension reduction method that determines large and high dimensional datasets’ structures. However, these nonlinear manifold learning methods, including isomap and locally linear embedding, are sensitive to noise. In this paper, we focus on the noisy nonlinear manifold learning method, such as Isomap. The main problem of the Isomap is sensitivity to noise. Our proposed new method noise removal isomap with a classification (NRIC), is based on the local tangent space alignment (LTSA) algorithm with classification techniques to remove noises and optimize neighborhood structure Isomap. The primary purpose of the NRIC is to increase efficiency, reduce noise, and improve the performance of the graph. Experiments on the real-world datasets have shown that the NRIC method outperforms efficiently and maintains an accurate low dimensional representation of the noisy nonlinear manifold learning data. The results show that LTSA with classification techniques provides high accuracy, mean-precision, mean-recall, and areas under the (ROC) curve (AUC) of the high dimensional datasets and optimizes the graphs.

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Funding

This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences (A Class) NO. XDA19020102.

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Authors and Affiliations

  1. School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Mahwish Yousaf, Tanzeel U. Rehman & Li Jing

  2. Key Laboratory of Strongly-Coupled Quantum Matter Physics Chinese Academy of Sciences Department of Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Muhammad Saadat Shakoor Khan

  3. School of Software,Taicang Campus, Northwestern Polytechnical University, Jiangsu, People’s Republic of China

    Shamsher Ullah

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  1. Mahwish Yousaf
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  2. Muhammad Saadat Shakoor Khan
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  4. Shamsher Ullah
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  5. Li Jing
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Correspondence to Li Jing.

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Yousaf, M., Khan, M.S.S., Rehman, T.U. et al. NRIC: A Noise Removal Approach for Nonlinear Isomap Method. Neural Process Lett 53, 2277–2304 (2021). https://doi.org/10.1007/s11063-021-10472-3

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