Scholarlink

<p>In this paper, we consider random <i>categorical</i> (i.e., discrete valued) datasets and study decompositions into batches of small sizes and reduced similarity. We propose <i>unique batch decompositions</i> (UBDs) to counter the effect of <i>pseudo-similar</i> data points and use a balls and bins argument to obtain high probability bounds for the minimum size of UBDs with a given strictness parameter. We then invoke martingale based methods to obtain bounds for the maximum size of similarity-free subsets, in terms of the average similarity probability and illustrate with an example, that the overall dataset itself could be similarity-free with high probability, i.e., with probability converging to one as the number of data points&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \rightarrow \infty .\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo stretchy="false">→</mo> <mi>∞</mi> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Reduced Similarity Decompositions and Subsets of Random Categorical Datasets

  • 期刊论文

  • 发表日期：

    2025年10月13日

查看全文
  • Ghurumuruhan Ganesan

摘要

In this paper, we consider random categorical (i.e., discrete valued) datasets and study decompositions into batches of small sizes and reduced similarity. We propose unique batch decompositions (UBDs) to counter the effect of pseudo-similar data points and use a balls and bins argument to obtain high probability bounds for the minimum size of UBDs with a given strictness parameter. We then invoke martingale based methods to obtain bounds for the maximum size of similarity-free subsets, in terms of the average similarity probability and illustrate with an example, that the overall dataset itself could be similarity-free with high probability, i.e., with probability converging to one as the number of data points  \(n \rightarrow \infty .\) n → ∞ .