The BAB algorithm for computing the total least trimmed squares estimator

2020 ◽  
Vol 94 (12) ◽  
Author(s):  
Zhipeng Lv ◽  
Lifen Sui
Keyword(s):  
Least Trimmed Squares

scholarly journals MUREN: a robust and multi-reference approach of RNA-seq transcript normalization

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Yance Feng ◽  
Lei M. Li
Keyword(s):  
Biological Significance ◽  
Housekeeping Genes ◽  
R Package ◽  
Data Sets ◽  
Statistical Regression ◽  
Rna Seq ◽  
Least Trimmed Squares ◽  
Standard Data ◽  
Wide Range ◽  
Multiple References

Abstract Background Normalization of RNA-seq data aims at identifying biological expression differentiation between samples by removing the effects of unwanted confounding factors. Explicitly or implicitly, the justification of normalization requires a set of housekeeping genes. However, the existence of housekeeping genes common for a very large collection of samples, especially under a wide range of conditions, is questionable. Results We propose to carry out pairwise normalization with respect to multiple references, selected from representative samples. Then the pairwise intermediates are integrated based on a linear model that adjusts the reference effects. Motivated by the notion of housekeeping genes and their statistical counterparts, we adopt the robust least trimmed squares regression in pairwise normalization. The proposed method (MUREN) is compared with other existing tools on some standard data sets. The goodness of normalization emphasizes on preserving possible asymmetric differentiation, whose biological significance is exemplified by a single cell data of cell cycle. MUREN is implemented as an R package. The code under license GPL-3 is available on the github platform: github.com/hippo-yf/MUREN and on the conda platform: anaconda.org/hippo-yf/r-muren. Conclusions MUREN performs the RNA-seq normalization using a two-step statistical regression induced from a general principle. We propose that the densities of pairwise differentiations are used to evaluate the goodness of normalization. MUREN adjusts the mode of differentiation toward zero while preserving the skewness due to biological asymmetric differentiation. Moreover, by robustly integrating pre-normalized counts with respect to multiple references, MUREN is immune to individual outlier samples.

Multi-Objective Genetic Algorithm for Robust Clustering with Unknown Number of Clusters

2012 ◽  
Vol 3 (1) ◽  
pp. 1-20
Author(s):  
Amit Banerjee
Keyword(s):  
Genetic Algorithm ◽  
Data Clustering ◽  
Optimal Number ◽  
Least Trimmed Squares ◽  
Cluster Assignment ◽  
Objective Criterion ◽  
Number Of Clusters ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Optimal Number Of Clusters

In this paper, a multi-objective genetic algorithm for data clustering based on the robust fuzzy least trimmed squares estimator is presented. The proposed clustering methodology addresses two critical issues in unsupervised data clustering – the ability to produce meaningful partition in noisy data, and the requirement that the number of clusters be known a priori. The multi-objective genetic algorithm-driven clustering technique optimizes the number of clusters as well as cluster assignment, and cluster prototypes. A two-parameter, mapped, fixed point coding scheme is used to represent assignment of data into the true retained set and the noisy trimmed set, and the optimal number of clusters in the retained set. A three-objective criterion is also used as the minimization functional for the multi-objective genetic algorithm. Results on well-known data sets from literature suggest that the proposed methodology is superior to conventional fuzzy clustering algorithms that assume a known value for optimal number of clusters.

scholarly journals Very High Density Point Clouds from UAV Laser Scanning for Automatic Tree Stem Detection and Direct Diameter Measurement

2020 ◽  
Vol 12 (8) ◽  
pp. 1236 ◽  
Author(s):  
Karel Kuželka ◽  
Martin Slavík ◽  
Peter Surový
Keyword(s):  
Cross Sections ◽  
Hough Transform ◽  
Laser Scanning ◽  
Point Clouds ◽  
Mean Bias Error ◽  
Bias Error ◽  
Least Trimmed Squares ◽  
Remotely Sensed Data ◽  
Individual Tree ◽  
Tree Stem

Three-dimensional light detection and ranging (LiDAR) point clouds acquired from unmanned aerial vehicles (UAVs) represent a relatively new type of remotely sensed data. Point cloud density of thousands of points per square meter with survey-grade accuracy makes the UAV laser scanning (ULS) a very suitable tool for detailed mapping of forest environment. We used RIEGL VUX-SYS to scan forest stands of Norway spruce and Scots pine, the two most important economic species of central European forests, and evaluated the suitability of point clouds for individual tree stem detection and stem diameter estimation in a fully automated workflow. We segmented tree stems based on point densities in voxels in subcanopy space and applied three methods of robust circle fitting to fit cross-sections along the stems: (1) Hough transform; (2) random sample consensus (RANSAC); and (3) robust least trimmed squares (RLTS). We detected correctly 99% and 100% of all trees in research plots for spruce and pine, respectively, and were able to estimate diameters for 99% of spruces and 98% of pines with mean bias error of −0.1 cm (−1%) and RMSE of 6.0 cm (19%), using the best performing method, RTLS. Hough transform was not able to fit perimeters in unfiltered and often incomplete point representations of cross-sections. In general, RLTS performed slightly better than RANSAC, having both higher stem detection success rate and lower error in diameter estimation. Better performance of RLTS was more pronounced in complicated situations, such as incomplete and noisy point structures, while for high-quality point representations, RANSAC provided slightly better results.

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