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Related Concept Videos

Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
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Published on: October 28, 2018

Probabilistic self-organizing maps for continuous data.

Ezequiel Lopez-Rubio1

  • 1Department of Computer Languages and Computer Science, University of Málaga, Málaga 29071, Spain. ezeqlr@lcc.uma.es

IEEE Transactions on Neural Networks
|August 24, 2010
PubMed
Summary
This summary is machine-generated.

Probabilistic self-organizing maps enhance computational intelligence by integrating probability distributions. This review unifies theoretical frameworks, exploring distributions, self-organization, and learning schemes for classification and visualization.

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Area of Science:

  • Computational Intelligence
  • Machine Learning
  • Data Mining

Background:

  • Original self-organizing feature maps lacked input space probability distributions.
  • Probabilistic methodologies offer significant advantages for self-organizing map models.
  • This has spurred diverse proposals in probabilistic computational intelligence.

Purpose of the Study:

  • To provide a comprehensive overview of probabilistic self-organizing maps.
  • To unify theoretical frameworks, including estimation theories.
  • To examine probability distributions, self-organization mechanisms, and learning schemes.

Main Methods:

  • Reviewing state-of-the-art probabilistic approaches to self-organizing maps.
  • Examining underlying estimation theories: Expectation Maximization and Stochastic Approximation.
  • Analyzing continuous probability distributions, self-organization mechanisms, and learning schemes.

Main Results:

  • Identified two main theoretical frameworks: Expectation Maximization and Stochastic Approximation.
  • Detailed common continuous probability distributions, self-organization mechanisms, and learning schemes.
  • Highlighted connections and relative advantages of different approaches.

Conclusions:

  • Probabilistic self-organizing maps represent a significant advancement in computational intelligence.
  • Understanding the interplay between distributions, mechanisms, and learning is crucial for optimal performance.
  • Evaluated performance in classification and visualization tasks, demonstrating practical utility.