Application of adaptive Laplacian Eigenmaps in near infrared spectral modeling

Laplacian Eigenmaps is a nonlinear dimensionality reduction algorithm based on graph theory. The algorithm adopted the Gaussian function to measure the affinity between a pair of points in the adjacency graph. However, the scaling parameter s in the Gaussian function is a hyper-parameter tuned empirically. Once the value of sigma is determined and fixed, the weight between two points depends wholly on the Euclidian distance between them, which is not suitable for multi-scale sample sets. To optimize the weight between two points in the adjacency graph and make the weight reflect the scale information of different sample sets, an adaptive LE improved algorithm is used in this paper. Considering the influence of adjacent sample points and multi-scale data, the Euclidean distance between the k-th nearest sample point to sample point x(i) is used as the local scaling parameter sigma(i) of x(i), instead of using a single scaling parameter sigma. The efficiency of the algorithm is testified by applying on two public near-infrared data sets. LE-SVR and ALE-SVR models are established after LE and ALE dimension reduction of SNV preprocessed data sets. Compared with the LE-SVR model, the R-2 and RPD of the ALE-SVR model established on the two data sets are improved, while RMSE is decreased, indicating that the prediction effect and stability of the regression model are established by the ALE algorithm are better than that of the traditional LE algorithm. Experiments show that the ALE algorithm can achieve a better dimensionality reduction effect than the LE algorithm.

Automated summary

Laplacian Eigenmaps is a nonlinear dimensionality reduction algorithm based on graph theory. In this paper, an adaptive LE improved algorithm is proposed to optimize the weight calculation by considering adjacent sample points and multi-scale data, achieving better dimensionality reduction effect.