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arXiv 2510.20107cs.LG
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关于加权维度的模式分类

On pattern classification with weighted dimensions

Aliah University(阿利亚大学)

Ayatullah Faruk Mollah

AI总结:

本文提出一种维度加权方案并整合到KNN分类器中,通过加权闵可夫斯基距离调节邻域形状,在基因表达等数据集上显著提升分类准确率约10%。

摘要:

在处理来自不同应用场景的多维样本时,对模式分类各个方面的研究往往是必不可少的。在此概念下,基于加权维度的距离度量一直是模式分析中的关键考量之一,因为它反映了样本之间的相似程度。尽管通常认为通过欧几里得距离的普遍使用已解决此问题,但大量问题仍时常浮现。在本文中,我们提出了:(a) 对距离度量范数和维度权重的影响及其可视化的详细分析;(b) 一种针对每个维度的新型加权方案;(c) 将此维度加权方案整合到KNN分类器中;以及(d) 使用所开发模型对多种合成和真实数据集进行模式分类。在与传统KNN在相同实验设置下的比较中,该模型在各种实验中表现良好。具体而言,对于基因表达数据集,在所有不同k值的交叉验证实验中,它都带来了显著且一致的分类准确率提升(约10%)。由于此类数据集包含的高维度样本数量有限,对最近邻进行有意义的选取是可取的,而这一需求通过所开发的加权方案和适当的范数来调节包含k个参考样本的区域形状和大小,得到了合理满足。因此,它构成了由加权闵可夫斯基距离驱动的KNN分类器的一个重要推广,并采用了当前的加权方案。

英文摘要:

Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of the vital considerations in pattern analysis as it reflects the degree of similarity between samples. Though it is often presumed to be settled with the pervasive use of Euclidean distance, plethora of issues often surface. In this paper, we present (a) a detail analysis on the impact of distance measure norms and weights of dimensions along with visualization, (b) a novel weighting scheme for each dimension, (c) incorporation of this dimensional weighting schema into a KNN classifier, and (d) pattern classification on a variety of synthetic as well as realistic datasets with the developed model. It has performed well across diverse experiments in comparison to the traditional KNN under the same experimental setups. Specifically, for gene expression datasets, it yields significant and consistent gain in classification accuracy (around 10%) in all cross-validation experiments with different values of k. As such datasets contain limited number of samples of high dimensions, meaningful selection of nearest neighbours is desirable, and this requirement is reasonably met by regulating the shape and size of the region enclosing the k number of reference samples with the developed weighting schema and appropriate norm. It, therefore, stands as an important generalization of KNN classifier powered by weighted Minkowski distance with the present weighting schema.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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