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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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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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The human nervous system handles vast amounts of information by translating sensory stimuli into neural impulses, which the brain processes, creating thoughts expressed through language or stored as memories. The brain also synthesizes information from emotions and memories, which significantly influence thoughts and behaviors. This intricate process creates a comprehensive mental picture.
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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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Learning Representation for Clustering Via Prototype Scattering and Positive Sampling.

Zhizhong Huang, Jie Chen, Junping Zhang

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    This study introduces ProPos, a novel deep clustering method that combines prototype scattering and positive sampling to overcome limitations of existing approaches. ProPos achieves state-of-the-art performance by ensuring uniform representations and improving cluster compactness.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Computer Vision

    Background:

    • Existing deep clustering methods utilize contrastive or non-contrastive representation learning.
    • Contrastive methods risk class collision due to negative pairs, while non-contrastive methods can lead to collapsed clusters.

    Purpose of the Study:

    • To develop a novel end-to-end deep clustering method, ProPos, that leverages the strengths of both contrastive and non-contrastive approaches.
    • To address class collision and representation collapse issues in deep clustering.

    Main Methods:

    • ProPos employs prototype scattering loss to maximize distances between prototypical representations, enhancing uniformity.
    • It utilizes positive sampling alignment to improve within-cluster compactness by matching augmented views with sampled neighbors.
    • The method is optimized within an end-to-end expectation-maximization framework.

    Main Results:

    • ProPos effectively avoids class collision and representation collapse.
    • The method achieves uniform representations with improved within-cluster compactness and well-separated clusters.
    • Experimental results show competing performance on moderate-scale datasets and state-of-the-art results on large-scale datasets.

    Conclusions:

    • ProPos offers a robust deep clustering solution by integrating prototype scattering and positive sampling.
    • The proposed method demonstrates superior performance, particularly on large-scale clustering tasks.
    • The availability of source code facilitates further research and application.