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Related Concept Videos

Maximizing the Directional Derivative01:25

Maximizing the Directional Derivative

The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...
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Related Experiment Video

Updated: Jun 20, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

Multi-directional search from the primitive initial point for Gaussian mixture estimation using variational Bayes

Yuta Ishikawa1, Ichiro Takeuchi, Ryohei Nakano

  • 1Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan. ishikawa@goat.ics.nitech.ac.jp

Neural Networks : the Official Journal of the International Neural Network Society
|September 1, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a novel multi-directional search method for Gaussian mixture model (GMM) estimation, improving upon existing variational Bayes (VB) techniques. The method effectively escapes local optima by utilizing saddle points for better GMM parameter estimation.

Related Experiment Videos

Last Updated: Jun 20, 2026

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine
08:27

Image Recognition and Parameter Analysis of Concrete Vibration State Based on Support Vector Machine

Published on: January 5, 2024

Area of Science:

  • Machine Learning
  • Statistical Modeling

Background:

  • Gaussian mixture models (GMMs) are versatile for approximating probability distributions.
  • Variational Bayes (VB) methods for GMM estimation often converge to local optima due to multimodal free energy functions.

Purpose of the Study:

  • To develop an alternative to the deterministic annealing VB (DAVB) method for improved GMM estimation.
  • To address the local optima problem in GMM estimation using VB.

Main Methods:

  • Proposed a multi-directional search from a primitive initial point (PIP), identified as a saddle point.
  • Utilized eigen-analysis of the Hessian matrix for efficient search from PIP neighborhoods.
  • Investigated the curvature of the free energy function.

Main Results:

  • The proposed method demonstrates effectiveness in GMM estimation.
  • Numerical experiments on real datasets validate the method's performance.
  • The primitive initial point (PIP) was identified as a saddle point.

Conclusions:

  • The novel multi-directional search method offers an effective alternative for GMM estimation.
  • The approach successfully navigates the complex free energy landscape to find better solutions.
  • This method enhances the capabilities of variational Bayes for GMM problems.