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The centroid is an important concept in engineering, physics, and mechanics. It is the geometric center of a body. It always lies within the body except in cases with holes or cavities. When the material that a body is composed of is uniform or homogeneous, the centroid coincides with its center of mass or the center of gravity.
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The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance point, and even its design. In this context, consider a thin wire bent in the form of a quarter circular arc. Polar coordinates are used to calculate the centroid. The wire is first divided into small differential elements of a length equal to the radius multiplied by the differential angle.
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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.
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Aggregate classification is generally based on its size, petrographic characteristics, weight, and source. Size classification ranges from coarse to fine aggregates, defined by the size of the particles. Coarse aggregates are particles that do not pass through ASTM sieve No. 4, and aggregates that pass through the sieve are fine aggregates.
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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: Aug 22, 2025

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Image Clustering Algorithm Based on Predefined Evenly-Distributed Class Centroids and Composite Cosine Distance.

Qiuyu Zhu1, Liheng Hu1, Rui Wang1

  • 1School of Communication & Information Engineering, Shanghai University, Shanghai 200444, China.

Entropy (Basel, Switzerland)
|November 11, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel image clustering algorithm using predefined evenly-distributed class centroids (PEDCC) and composite cosine distance. The method enhances deep learning-based clustering accuracy for complex natural images.

Keywords:
clusteringcomposite cosine distancecontrastive learningpredefined evenly-distributed class centroids (PEDCC)

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Machine Learning

Background:

  • Deep neural network-based clustering algorithms aim to optimize feature representation for accurate image clustering.
  • Existing methods struggle with low accuracy when dealing with complex natural images.

Purpose of the Study:

  • To develop an improved image clustering algorithm for complex natural images.
  • To enhance clustering accuracy by introducing predefined evenly-distributed class centroids (PEDCC) and composite cosine distance.

Main Methods:

  • Designed an encoder-only network structure with normalized latent features.
  • Replaced Euclidean distance with composite cosine distance in two latent feature space loss functions.
  • Utilized contrastive learning and a self-supervised pretrained model.

Main Results:

  • Contrastive learning significantly improves latent feature learning quality.
  • Composite cosine distance is more suitable than Euclidean distance for normalized latent features and PEDCC-based Maximum Mean Discrepancy (MMD) loss.
  • Self-supervised pretraining effectively boosts clustering performance on complex natural images.

Conclusions:

  • The proposed image clustering algorithm achieves superior performance compared to state-of-the-art methods.
  • The combination of normalized latent features, composite cosine distance, and PEDCC is effective for image clustering.
  • Contrastive learning and self-supervised pretraining are crucial for enhancing clustering accuracy in deep learning models.