以最近鄰居距離作高維度空間密度估計

Abstract

密度估計的研究發展出許多演算法，對於各樣科系的資料分析都有極大的影響力。但是密度估計對於在高維度的資料卻表現不佳。這篇研究探討傳統的密度估計運在高維度資料的遇到的問題，為什麼密度估計所出來的結果可能極低到會被雜訊影像或級高到無法做適當的比較。這篇研究提出在高維資料中若資料的維度不確定的時候應該運用負距離最鄰近資料的對數來做密度的估計。這篇研究也將所提出的演算法用在接近十萬維度的資料上，並且有良好的表現。

The study of density estimation has produced algorithms that has been used across many disciplines and has become a common fixture in the analysis of data. However density estimation has not been able to perform well on high-dimensional datasets. In this study, we discuss the reasons that traditional density estimation would not work well for high dimensional data. Why they give values that are uninterpretable, with either the values so low that the values may be greatly affected by the model noise or computational noise, or the values are so high where we cannot compute the ratio of infinity over infinity. This study proposes using negative log distance to k nearest neighbors as the metric to compare when the dimension of the samples are not known. The resulting classifier, HDDE, was used to classify images in domains with close to 100k dimensions with reasonable results.