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Related Concept Videos

Transformations of Functions III01:20

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
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Microbial communities are dynamic environments where cell lysis releases free DNA into the surroundings. Other cells can take up this extracellular DNA through a process known as transformation.When a cell incorporates this foreign DNA into its genome, resulting in genetic modification, the process is known as transformation. Cells capable of this process are termed competent. Competence can be natural, as observed in certain bacteria and archaea, or artificially induced in the...
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Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
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Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...
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A Swin Transformer-Based Model for Thyroid Nodule Detection in Ultrasound Images
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Graph transform learning.

Angshul Majumdar1

  • 1Indraprastha Institute of Information Technology, Delhi, 110020, India.

Neural Networks : the Official Journal of the International Neural Network Society
|May 27, 2020
PubMed
Summary
This summary is machine-generated.

Graph transform learning, a novel representation learning approach, analyzes data correlations using graph Laplacians. This method is applied to clustering and solving inverse problems for enhanced data analysis.

Keywords:
ClusteringGraphical modelSignal processingTransform learning

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Area of Science:

  • Machine Learning
  • Data Science
  • Graph Theory

Background:

  • Representation learning aims to discover meaningful data features.
  • Transform learning is a framework for learning operators to generate data representations.
  • Existing methods may not fully leverage inherent data correlations.

Purpose of the Study:

  • Introduce graph transform learning, a variant of transform learning.
  • Incorporate dataset correlations via graph Laplacians into the learning process.
  • Develop two distinct approaches for applying graph transform learning.

Main Methods:

  • Propose a first variant where the graph is computed from data and remains fixed.
  • Propose a second variant where the graph is learned iteratively during the operation.
  • Apply the first variant to clustering tasks.
  • Apply the second variant to solving inverse problems.

Main Results:

  • Demonstrate the effectiveness of graph transform learning in representation learning.
  • Showcase successful application of the fixed-graph approach for clustering.
  • Highlight the utility of the iterative-graph approach for inverse problems.

Conclusions:

  • Graph transform learning offers a powerful new framework for representation learning.
  • Explicitly modeling data correlations through graph Laplacians enhances analytical capabilities.
  • The developed variants provide versatile tools for both clustering and inverse problem-solving.