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Related Concept Videos

Active Filters01:25

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
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:
Passive Filters01:27

Passive Filters

Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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...
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...

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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data
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CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data

Published on: November 10, 2023

Unconstrained correlation filters.

A Mahalanobis, B V Vijaya Kumar, S Song

    Applied Optics
    |October 2, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new correlation filter design that significantly improves distortion tolerance. The advanced filters maintain key features of earlier models while offering better performance and computational efficiency.

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    Area of Science:

    • Computer Vision
    • Signal Processing
    • Pattern Recognition

    Background:

    • Correlation filters are crucial for object recognition.
    • Existing methods like minimum average correlation energy (MACE) and minimum variance synthetic discriminant function (MVSDF) have limitations in distortion tolerance.
    • Optimizing filter performance requires addressing output constraints.

    Purpose of the Study:

    • To develop a novel correlation filter with enhanced distortion tolerance.
    • To generalize the minimum average correlation energy criterion for improved performance measurement.
    • To unify existing filter formulations and explore their interrelationships.

    Main Methods:

    • Mathematical analysis of distortion tolerance in correlation filters.
    • Modification of the synthetic discriminant function formulation by removing hard output constraints.
    • Development of a filter design algorithm using simple statistical parameters and diagonal matrix inversion.

    Main Results:

    • The proposed filters demonstrate superior distortion tolerance compared to predecessors.
    • The new approach unifies several existing correlation filter theories.
    • The filter design algorithm is computationally efficient.

    Conclusions:

    • Removing hard constraints in filter design leads to improved distortion tolerance.
    • The generalized minimum average correlation energy criterion is a robust measure of performance.
    • The proposed filters offer a computationally attractive and high-performing solution for pattern recognition tasks.