RELIABILITY OF OPTIMAL LINEAR PROJECTION OF GROWING SCALE-FREE NETWORKS

Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, this is called Truncated Singular Value Decomposition (TSVD). In situations where the data is continuously changing, the projection might become obsolete. Since the change rate of data can be fast, it is an interesting question whether the TSVD projection of the initial data is reliable. In the case of complex networks, this scenario is particularly important when considering network growth. Here we study the reliability of the TSVD projection of growing scale-free networks, monitoring its evolution at global and local scales.

Download Full-text

Using Singular Value Decomposition to Reduce Dimensionality of Initial Data Set

2020 61st International Scientific Conference on Information Technology and Management Science of Riga Technical University (ITMS) ◽

10.1109/itms51158.2020.9259304 ◽

2020 ◽

Author(s):

Oleg Uzhga-Rebrov ◽

Galina Kuleshova

Keyword(s):

Singular Value Decomposition ◽

Initial Data ◽

Singular Value ◽

Data Set ◽

Value Decomposition

Download Full-text

Distribution-free multiple imputation in an interaction matrix through singular value decomposition

Scientia Agricola ◽

10.1590/s0103-90162008000400015 ◽

2008 ◽

Vol 65 (4) ◽

pp. 422-427 ◽

Cited By ~ 9

Author(s):

Genevile Carife Bergamo ◽

Carlos Tadeu dos Santos Dias ◽

Wojtek Janusz Krzanowski

Keyword(s):

Singular Value Decomposition ◽

Multiple Imputation ◽

Missing Values ◽

Eucalyptus Grandis ◽

Singular Value ◽

Data Matrix ◽

Interaction Matrix ◽

General Measure ◽

Data Set ◽

Value Decomposition

Some techniques of multivariate statistical analysis can only be conducted on a complete data matrix, but the process of data collection often misses some elements. Imputation is a technique by which the missing elements are replaced by plausible values, so that a valid analysis can be performed on the completed data set. A multiple imputation method is proposed based on a modification to the singular value decomposition (SVD) method for single imputation, developed by Krzanowski. The method was evaluated on a genotype × environment (G × E) interaction matrix obtained from a randomized blocks experiment on Eucalyptus grandis grown in multienvironments. Values of E. grandis heights in the G × E complete interaction matrix were deleted randomly at three different rates (5%, 10%, 30%) and were then imputed by the proposed methodology. The results were assessed by means of a general measure of performance (Tacc), and showed a small bias when compared to the original data. However, bias values were greater than the variability of imputations relative to their mean, indicating a smaller accuracy of the proposed method in relation to its precision. The proposed methodology uses the maximum amount of available information, does not have any restrictions regarding the pattern or mechanism of the missing values, and is free of assumptions on the data distribution or structure.

Download Full-text

Singular Value Decomposition Based Features for Automatic Tumor Detection in Wireless Capsule Endoscopy Images

Applied Bionics and Biomechanics ◽

10.1155/2016/3678913 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Vahid Faghih Dinevari ◽

Ghader Karimian Khosroshahi ◽

Mina Zolfy Lighvan

Keyword(s):

Singular Value Decomposition ◽

Capsule Endoscopy ◽

Color Space ◽

Wireless Capsule Endoscopy ◽

Singular Value ◽

Support Vector ◽

Discrete Wavelet ◽

Data Set ◽

Value Decomposition ◽

Wireless Capsule

Wireless capsule endoscopy (WCE) is a new noninvasive instrument which allows direct observation of the gastrointestinal tract to diagnose its relative diseases. Because of the large number of images obtained from the capsule endoscopy per patient, doctors need too much time to investigate all of them. So, it would be worthwhile to design a system for detecting diseases automatically. In this paper, a new method is presented for automatic detection of tumors in the WCE images. This method will utilize the advantages of the discrete wavelet transform (DWT) and singular value decomposition (SVD) algorithms to extract features from different color channels of the WCE images. Therefore, the extracted features are invariant to rotation and can describe multiresolution characteristics of the WCE images. In order to classify the WCE images, the support vector machine (SVM) method is applied to a data set which includes 400 normal and 400 tumor WCE images. The experimental results show proper performance of the proposed algorithm for detection and isolation of the tumor images which, in the best way, shows 94%, 93%, and 93.5% of sensitivity, specificity, and accuracy in the RGB color space, respectively.

Download Full-text