Assessment of local covariance estimation through Least Squares Collocation over Iran

Covariance determination as the heart of Least Squares Collocation gravity field modeling is based on fitting an analytical covariance to the empirical covariance, which is stemmed from gravimetric data. The main objective of this study is to process different local covariance strategies over four regions with different topography and spatial data distribution in Iran. For this purpose, Least Squares Collocation based on Remove – Compute – Restore technique is implemented. In the Remove step, gravity reduction in regions with a denser distribution and a rougher topography is more effective. In the Compute step, the assessment of the Collocation estimates on the gravity anomaly control points illustrates that data density is more relevant than topography roughness to have a good covariance determination. Moreover, among the different attempts of localizing the covariance estimation, a recursive approach correcting the covariance parameters based on the agreement between Least Squares Collocation estimates and control points shows better performance. Furthermore, we could see that covariance localization in a region with sparse or bad distributed observations is a challenging task and may not necessarily improve the Collocation gravity modeling. Indeed, the geometrical fitness of the empirical and analytical covariances – which is usually a qualitative test to verify the precision of the covariance determination – is not always an adequate criterion.

A new local covariance matrix estimation for the classification of gene expression profiles in RNA-Seq data

Background and ObjectiveRecent developments in the next-generation sequencing (NGS) based on RNA-sequencing (RNA-Seq) allow researchers to measure the expression levels of thousands of genes for multiple samples simultaneously. In order to analyze these kind of data sets, many classification models have been proposed in the literature. Most of the existing classifiers assume that genes are independent; however, this is not a realistic approach for real RNA-Seq classification problems. For this reason, some other classification methods, which incorporates the dependence structure between genes into a model, are proposed. qtQDA proposed by Koçhan et al. [1] is one of those classifiers, which estimates covariance matrix by Maximum Likelihood Estimator.MethodsIn this study, we use a another approach based on local dependence function to estimate the covariance matrix to be used in the qtQDA classification model. We investigate the impact of different covariance estimates on RNA-Seq data classification.ResultsThe performances of qtQDA classifier based on two different covariance matrix estimates are compared over two real RNA-Seq data sets, in terms of classification error rates. The results show that using local dependence function approach yields a better estimate of covariance matrix and increases the performance of qtQDA classifier.ConclusionIncorporating the true/accurate covariance matrix into the classification model is an important and crucial step particularly for cancer prediction. The local covariance matrix estimate allows researchers to classify cancer patients based on gene expression profiles more accurately. R code for local dependence function is available at https://github.com/Necla/LocalDependence.

A Novel Hyperspectral Image Classification Pattern Using Random Patches Convolution and Local Covariance

Today, more and more deep learning frameworks are being applied to hyperspectral image classification tasks and have achieved great results. However, such approaches are still hampered by long training times. Traditional spectral–spatial hyperspectral image classification only utilizes spectral features at the pixel level, without considering the correlation between local spectral signatures. Our article has tested a novel hyperspectral image classification pattern, using random-patches convolution and local covariance (RPCC). The RPCC is an effective two-branch method that, on the one hand, obtains a specified number of convolution kernels from the image space through a random strategy and, on the other hand, constructs a covariance matrix between different spectral bands by clustering local neighboring pixels. In our method, the spatial features come from multi-scale and multi-level convolutional layers. The spectral features represent the correlations between different bands. We use the support vector machine as well as spectral and spatial fusion matrices to obtain classification results. Through experiments, RPCC is tested with five excellent methods on three public data-sets. Quantitative and qualitative evaluation indicators indicate that the accuracy of our RPCC method can match or exceed the current state-of-the-art methods.