The Correlation Analysis Of Remote Sensing Data Sets Based On Sparse Representation

In recent years, with the development of technology for earth observation, remote sensing data resources are richer and richer. How to mine and analyze the data to gain new model, new knowledge and new laws of data becomes very popular in knowledge discovery field. Correlation analysis of the data sets is of great significance to knowledge discovery.The volume of remote sensing data is very huge. Using the software to analyze the correlation of data sets in spatial domain needs to put all the data at one time. So it costs a lot of time and memory spaces. When the data sharp increase, software may face crash. To compress data and simplify the correlation analysis, the data should be transformed to sparse domain.There are mainly two types of dictionary for sparse representation:analytical and non-analytical. Firstly, wavelet of analytical dictionary was used to represent different bands and different textures data sets. We statistic analyzed the high frequency part of wavelet coefficients and make the probability density distribution curve.From the experiment results we obtained that the high frequency part of the wavelet coefficients satisfy Gaussian mixture model, the curve has fat tails characteristic and there are too many non-zero elements. Wavelet is not suitable for sparse representing remote sensing data with complex textures.Then the paper use non-analytical dictionary to sparse represent the data set. The volume of remote sensing data is large, so dictionary construction algorithm should be applied to big data; To simplify subsequent correlation analysis, representation should preserve the original data correlation information. Existing algorithms can’t meet the two requirements at the same time. Combining the idea of hypergraph sparse coding and increment learning, dynamic hypergraph sparse coding algorithm was proposed. The algorithm divided all the data into several blocks. When a training block was inputted, we constructed a correlation matrix and selectively added some dictionary atoms based on this training block, With the increase of input training blocks, the algorithm achieves the dynamic update of dictionary.When the data sets were transformed to sparse domain, the formula for calculating the correlation coefficient in spatial domain was no longer valid. In order to measure the correlation between the original data set, we need to define a formula to measure the correlation in sparse domain.This paper defines a projection matrix. Based on the idea of dictionary learning, we update the projection matrix and sparse coefficients alternately. The correlation coefficients calculated in spatial domain were used to guide the whole process of learning, so that the projection of the difference between every two sparse coefficients under the projection matrix is approximately equal to the correlation coefficient calculated in spatial domain.Finally, we chose the nationwide population, GDP, construction land area data and so on in year2000for the experiments. First, we transformed these data sets into sparse domain and compared our results with the results of ODL, RLS algorithm. Under the premise of the same reconstruction precision with RLS, dynamic hypergraph coding greatly reducing the running time. Then we analyzed the correlation between different data sets in sparse domain and compared with the results calculated in spatial domain. Experimental results show that correlation coefficients calculated in two domains approximately satisfy a linear relationship.