Related Experiment Video
Updated: May 16, 2026
14:27
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
Published on: June 26, 2013
Generating correlation matrices based on the boundaries of their coefficients.
Kawee Numpacharoen1, Amporn Atsawarungruangkit
1Financial Product Development, Kasikorn Securities, Bangkok, Thailand. kawee.num@student.mahidol.ac.th
Plos One
|November 16, 2012
Summary
This study introduces an efficient algorithm for generating correlation matrices from bounded random variables. The method produces more extreme variable relationships, beneficial for complex systems modeling.
Area of Science:
- Statistics and Probability
- Computational Mathematics
Background:
- Correlation matrices are fundamental for describing relationships among multiple variables across diverse fields like finance, engineering, statistics, and medicine.
- Existing methods for generating correlation matrices may not capture extreme relationships effectively.
Purpose of the Study:
- To develop an efficient sequential method for determining theoretical bounds of correlation coefficients.
- To propose an algorithm for generating n x n correlation matrices using any bounded random variables.
Main Methods:
- Sequential calculation of theoretical bounds for correlation coefficients.
- Algorithm for constructing n x n correlation matrices using specified bounded random variables.
- Utilizing uniform random variables as a case study for matrix generation.
Main Results:
- The proposed algorithm efficiently generates correlation matrices.
- Matrices generated using uniform random variables exhibit more extreme variable relationships compared to other methods.
- Demonstrated the ability to model complex systems where rare events are significant.
Conclusions:
- The novel method provides a way to obtain theoretical bounds and generate correlation matrices.
- The generated matrices with extreme relationships are valuable for modeling complex systems, particularly in biological sciences.
- Offers a flexible approach applicable to various bounded random variables.
More Related Videos
Related Concept Videos
01:14Extraction: Partition and Distribution Coefficients
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
For extracting a solute from an aqueous phase into an organic...
01:11Calculating and Interpreting the Linear Correlation Coefficient
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
01:12Coefficient of Correlation
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...
01:10Calibration Curves: Correlation Coefficient
In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
01:08Vector Algebra: Method of Components
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
In many applications, the magnitudes and directions of...
01:24Area Computation by the Alternative Coordinate Method
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...