NRIC: A Noise Removal Approach for Nonlinear Isomap Method

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.