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Related Concept Videos

Coefficient of Correlation01:12

Coefficient 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...
Kendall's Coefficient of Concordance01:20

Kendall's Coefficient of Concordance

Kendall's Coefficient of Concordance (W), also known as Kendall's W, is a non-parametric statistical measure used to assess the agreement or concordance between multiple raters or judges when they rank a set of items. It is often used when you have ordinal data (ranks) and you want to see if there is consistency or consensus among the raters. It is widely applied in research areas such as psychology, medicine, and social sciences, where multiple judges are asked to rank or rate subjects or...
Calibration Curves: Correlation Coefficient01:10

Calibration 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...
Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating 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:
Correlation01:09

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:

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Related Experiment Videos

A new validity measure for a correlation-based fuzzy c-means clustering algorithm.

Mingrui Zhang1, Wei Zhang, Hugues Sicotte

  • 1Computer Science Department, Winona State University, MN 55987, USA. mzhang@winona.edu

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
|December 8, 2009
PubMed
Summary
This summary is machine-generated.

Assessing cluster quality in unsupervised learning is difficult. This study introduces a new fuzzy clustering validity measure using Pearson correlation, improving consistency across microarray datasets.

Related Experiment Videos

Area of Science:

  • Computational Biology
  • Data Science
  • Bioinformatics

Background:

  • Unsupervised clustering is vital for analyzing complex datasets like microarrays.
  • Evaluating the quality of clusters formed by clustering algorithms remains a significant challenge.
  • Existing validity measures for fuzzy clustering may lack consistency across different data types.

Purpose of the Study:

  • To address the challenge of assessing cluster quality in unsupervised clustering.
  • To develop and evaluate a novel validity measure for fuzzy c-means algorithms.
  • To improve the reliability of cluster quality assessment in biological data analysis.

Main Methods:

  • Developed a new fuzzy clustering validity measure incorporating Pearson correlation into distance metrics.
  • Designed the measure based on within-cluster sum of squares and fuzzy membership values.
  • Evaluated the new measure against existing fuzzy partition coefficient and fuzzy validity index.

Main Results:

  • The novel validity measure demonstrated consistent performance across six diverse microarray datasets.
  • The proposed measure showed improved or comparable results to existing indices.
  • The measure effectively assesses the validity of fuzzy clusters generated by correlation-based fuzzy c-means.

Conclusions:

  • The newly developed validity measure offers a reliable approach for assessing fuzzy cluster quality.
  • This measure is particularly useful for correlation-based fuzzy c-means algorithms.
  • Consistent performance across microarray data suggests broad applicability in bioinformatics.