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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Maxam-Gilbert Sequencing01:05

Maxam-Gilbert Sequencing

In the same year as the discovery of the Sanger sequencing method, another group of scientists, Allan Maxam and Walter Gilbert, demonstrated their chemical-cleavage method for DNA sequencing. The Maxam-Gilbert method relies on using different chemicals that can cleave the DNA sequence at specific sites, the separation of resulting DNA fragments of variable size using electrophoresis, and deciphering the DNA sequence from the resulting gel bands.
Challenges of the Maxam-Gilbert Method
The...
Multiple Comparison Tests01:13

Multiple Comparison Tests

Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
It would be easy to compare two samples using a significance alpha level of 0.05. In other words, there is only one sample pair to be compared. However, it would be difficult to identify a significantly different sample if the number...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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Related Experiment Video

Updated: Jul 15, 2026

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
12:27

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

Multi-view Clustering with Cauchy-Schwarz Mutual Information Maximin.

Zhen Tian, Enlai Ouyang, Quan Zou

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |July 13, 2026
    PubMed
    Summary

    This study introduces a new Cauchy-Schwarz Mutual Information Maximin (CS-MIM) method for deep multi-view clustering. CS-MIM accurately estimates mutual information without variational inference, improving clustering performance.

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    Cross-Modal Multivariate Pattern Analysis
    13:51

    Cross-Modal Multivariate Pattern Analysis

    Published on: November 9, 2011

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    Last Updated: Jul 15, 2026

    Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
    12:27

    Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

    Published on: February 15, 2017

    Cross-Modal Multivariate Pattern Analysis
    13:51

    Cross-Modal Multivariate Pattern Analysis

    Published on: November 9, 2011

    Area of Science:

    • Machine Learning
    • Information Theory
    • Computer Vision

    Background:

    • Deep multi-view clustering (MVC) utilizes information bottleneck (IB) for optimizing data compression and feature preservation.
    • Existing IB-based MVC methods often rely on variational inference for mutual information (MI) estimation, leading to potential errors and instability.
    • This limits the effectiveness of deep MVC in capturing complex multi-view relationships.

    Purpose of the Study:

    • To develop a novel method for direct and stable mutual information estimation in deep multi-view clustering.
    • To enhance the performance of multi-view clustering by improving the information bottleneck principle.
    • To introduce a new approach for modeling multi-view information and cross-view complementarity.

    Main Methods:

    • Proposed a Cauchy-Schwarz Mutual Information Maximin (CS-MIM) method for direct MI estimation using closed-form expressions.
    • Introduced a non-parametric MI estimation using Cauchy-Schwarz (CS) divergence with multi-kernel Gram matrices, avoiding variational inference errors.
    • Developed a MI maximin mechanism with analytical gradients for effective data compression and feature preservation within the IB framework.
    • Designed a cross-view adaptive attention (CAA) mechanism guided by CS divergence-based MI to capture inter-view complementarity.

    Main Results:

    • The CS-MIM method directly estimates MI without relying on variational inference, ensuring stability and accuracy.
    • The proposed approach effectively compresses multi-view data while preserving essential features through an analytical gradient-based MI maximin mechanism.
    • The cross-view adaptive attention mechanism successfully captures complementary information across different views.
    • Empirical evaluations on 12 datasets show that CS-MIM significantly outperforms state-of-the-art methods in multi-view clustering.

    Conclusions:

    • The CS-MIM method offers a more stable and accurate approach to mutual information estimation for deep multi-view clustering.
    • This novel method enhances the information bottleneck principle by providing direct MI estimation and analytical gradients.
    • The study demonstrates the effectiveness of CS-MIM in improving multi-view clustering performance, particularly in capturing cross-view relationships.