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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.
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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.
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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...
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Spearman's rank correlation test, also known as Spearman's rho, is a nonparametric method for assessing the strength and direction of association between two variables. This test is particularly valuable when the data distribution is unknown or when the assumption of normality does not hold. Named after the English psychologist and statistician Dr. Charles Edward Spearman, it serves as the nonparametric counterpart to Pearson's correlation coefficient.
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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Tensor canonical correlation analysis.

Eun Jeong Min1, Eric C Chi2, Hua Zhou3

  • 1Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, 19104, PA, U.S.A.

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|July 14, 2020
PubMed
Summary
This summary is machine-generated.

Tensor Canonical Correlation Analysis (TCCA) extends classic methods for analyzing complex tensor data from fields like neuroimaging. This new approach effectively discovers relationships within multidimensional arrays, offering improved stability and efficiency.

Keywords:
CP decompositionblock coordinate ascentmultidimensional array data

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Area of Science:

  • Multivariate Statistics
  • Data Analysis
  • Machine Learning

Background:

  • Canonical Correlation Analysis (CCA) is limited with modern high-dimensional tensor data.
  • Neuroimaging and remote sensing generate complex multidimensional array data.
  • Existing methods struggle with the structure and dimensionality of tensor datasets.

Purpose of the Study:

  • Introduce Tensor Canonical Correlation Analysis (TCCA) for analyzing relationships between two tensors.
  • Preserve the inherent multidimensional structure of tensor data.
  • Develop a statistically robust and computationally efficient method for tensor data analysis.

Main Methods:

  • Developed Tensor Canonical Correlation Analysis (TCCA) to handle multidimensional tensor data.
  • Incorporated a parsimonious covariance structure for enhanced stability and efficiency.
  • Proposed efficient estimation algorithms with global convergence guarantees.
  • Described a probabilistic model for TCCA for synthetic data generation.

Main Results:

  • TCCA effectively discovers relationships between two tensors while preserving their multidimensional structure.
  • The proposed methods utilize fewer parameters compared to traditional approaches.
  • Parsimonious covariance structures improve stability and efficiency.
  • Simulation studies demonstrate the effectiveness of the TCCA methods.

Conclusions:

  • TCCA provides a powerful new tool for analyzing complex relationships in multidimensional tensor data.
  • The method offers advantages in parameter efficiency, stability, and computational performance.
  • TCCA is applicable to modern datasets from fields like neuroimaging and remote sensing.