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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

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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...
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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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One-Way ANOVA: Equal Sample Sizes01:15

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
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One-Way ANOVA: Unequal Sample Sizes01:15

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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The theory of catalytically perfect enzymes was first proposed by W.J. Albery and J. R. Knowles in 1976. These enzymes catalyze biochemical reactions at high-speed. Their catalytic efficiency values range from 108-109 M-1s-1. These enzymes are also called 'diffusion-controlled' as the only rate-limiting step in the catalysis is that of the substrate diffusion into the active site. Examples include triose phosphate isomerase, fumarase, and superoxide dismutase.
 
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Support reactions in three dimensions help maintain the stability and equilibrium of various structures and systems. These reactions prevent the system from translating and rotating, ensuring the design can withstand external forces and perform its intended function efficiently and safely. Some of the supports providing support reactions in three dimensions are discussed below:
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Related Experiment Video

Updated: Jan 25, 2026

Stable Aqueous Suspensions of Manganese Ferrite Clusters with Tunable Nanoscale Dimension and Composition
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On Perfect Clustering of High Dimension, Low Sample Size Data.

Soham Sarkar, Anil K Ghosh

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |April 28, 2019
    PubMed
    Summary

    Clustering high-dimensional data is challenging. A new measure, MADD, improves clustering performance and cluster number estimation in high dimension, low sample size (HDLSS) situations.

    Area of Science:

    • Statistics
    • Data Mining
    • Machine Learning

    Background:

    • Traditional clustering algorithms struggle with high-dimensional, low-sample-size (HDLSS) data due to distance concentration and neighborhood structure issues.
    • Euclidean distance-based methods are particularly affected, leading to poor performance in these scenarios.

    Purpose of the Study:

    • To introduce and evaluate a novel data-driven dissimilarity measure, MADD (Measure of Aggregated Dissimilarity Distance), designed to overcome HDLSS challenges in clustering.
    • To demonstrate the effectiveness of MADD in improving clustering performance and cluster number estimation for high-dimensional datasets.

    Main Methods:

    • Development of the MADD dissimilarity measure, leveraging the distance concentration phenomenon in high dimensions.
    • Theoretical and numerical studies to validate MADD's performance against traditional distance measures.

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  • Adaptation and creation of cluster number estimation algorithms, incorporating MADD for enhanced high-dimensional performance.
  • Analysis of simulated and real-world datasets to showcase MADD's practical utility.

    • Main Results:

    • Clustering algorithms utilizing MADD exhibit superior performance in high-dimensional, low-sample-size (HDLSS) settings compared to those using standard distance functions.
    • MADD effectively addresses the adverse effects of distance concentration and neighborhood structure violations.
    • Existing cluster number estimation algorithms show improved accuracy when integrated with MADD.
    • A new, consistent estimator for the number of clusters in the HDLSS regime was developed and validated.

    Conclusions:

    • The MADD dissimilarity measure offers a robust solution for clustering high-dimensional data, particularly in HDLSS scenarios.
    • MADD enhances the performance of both clustering algorithms and cluster number estimation techniques.
    • This approach provides a valuable tool for effective cluster analysis in complex, high-dimensional datasets.