Research On Locally Weighted Linear Model And Its Application To Spectral Reflectance Reconstruction

In supervised learning,such as classification and regression,the main aim is to learn the functional relationship between input and output variables,so that it can be used to predict the corresponding output of the measured input values.In practical application,it is often a complex nonlinear relationship.Global learning method directly using all the training samples to build the nonlinear relationship between input and output values,for a better learning result,it depends not only on methods with strong nonlinear learning ability,such as BP neural network,support vector machine and deep neural network and also rely on a large number of well-distributed training samples.And the complexity of model is difficult to control,few uneven distributed training samples and over-complicate models will both lead to over-fitting,while under-complicate models will lead to under-fitting.According to the principle of the locally linear embedding method in manifold learning,the local linear model assumes that the high-dimensional output variables can be represented by the linear combination of neighboring points in the local scope,and the corresponding input variables in the low-dimensional space also have a similar linear combination relationship.By using the linear combination of nearest neighbor points to estimate the test points,the local linear model avoids the dependence on the sample distribution and the selection of model complexity,which can prevent the model from over-fitting on a certain extent.Moreover,it is very suitable for dealing with the increasing online learning problem of training samples,so it received widely attention.However,the local linear model only relies on a few nearest neighbor points to construct the local reconstruction relationship,each nearest neighbor point plays an equal role in the construction of the model.If there are singularity or error points,it will have a huge impact on the model and make the model deviate from the real situation,which means the under-fitting.Although the regularization method can prevent the model from getting too close to the training points and enhance the generalization ability of the model by limiting the coefficient of the model,but the contribution of each neighbor point to the model is still the same.In order to solve the problem that local linear models are vulnerable to the exceptional points,this paper proposes two different local weighted linear models.According to the similarity of neighboring points with the test point,different weights are given to each neighboring point.Improve the contribution of high similarity neighbors to the model and reduce the impact of error points.Spectral reflectance is the ratio of the reflection of light waves on the surface of object in the visible wavelength range,and it is the physical property that determines the color of an object.Knowing the spectral reflectance information of the object,we can accurately reproduce the color of the object under arbitrary illumination and observation perspective.It has great significance to the industries which need high color accuracy,such as printing,painting,clothing,digital archiving of artworks,etc.Although a professional spectrophotometer can be used to measure the spectral reflectivity of an object,but it can’t be widely use due to the high price,complex operation,low measurement resolution and longtime operation.By establishing a functional relationship between the RGB values obtained by ordinary digital cameras and the high-dimensional spectral reflectance vectors,the spectral reflectance corresponding to the RGB pixel points can be reconstructed.The monetary cost and time cost of obtaining the spectral reflectance can be greatly reduced.How to design an accurate and efficient spectral reflectance reconstruction algorithm has attracted the attention of many experts and scholars.In this paper,the local weighted linear model is used for spectral reflectance reconstruction,and compared with the traditional global kernel regression method and local linear model to verify the effectiveness of the local weighted linear mode.In the experiment,different groups of experimental data were set up,and the reconstruction results of various models were compared in an all-round way.Finally,the experimental results show that the locally weighted linear model can effectively reduce the reconstruction error and obtain more accurate results.