發(fā)布時間：2019-07-11 20:06

【摘要】：降維是大數(shù)據(jù)分析和可視化領(lǐng)域中的核心問題,其中基于概率分布模型的降維算法通過最優(yōu)化高維數(shù)據(jù)模型和低維數(shù)據(jù)模型之間的代價函數(shù)來實現(xiàn)降維。這種策略的核心在于構(gòu)建最能體現(xiàn)數(shù)據(jù)特征的概率分布模型�；诖�,將Wasserstein距離引入降維,提出一個基于Wasserstein距離概率分布模型的非線性降維算法W-map。Wmap模型在高維數(shù)據(jù)空間和其相關(guān)對應(yīng)的低維數(shù)據(jù)空間建立相似的Wasserstein流,將降維轉(zhuǎn)化為最小運輸問題。在解決Wasserstein距離最小化的問題同時,依據(jù)數(shù)據(jù)的Wasserstein流模型在高維空間與其在低維空間相同的原則,尋找最匹配的低維數(shù)據(jù)投射。三組針對不同數(shù)據(jù)集的實驗結(jié)果表明W-map相對傳統(tǒng)概率分布模型可以產(chǎn)生正確性高且魯棒性好的高維數(shù)據(jù)降維可視化結(jié)果。
[Abstract]:Dimension reduction is the core problem in the field of big data analysis and visualization, in which the dimension reduction algorithm based on probability distribution model realizes dimension reduction by optimizing the cost function between high dimensional data model and low dimensional data model. The core of this strategy is to construct the probability distribution model which can best reflect the data characteristics. Based on this, the Wasserstein distance is introduced into dimension reduction, and a nonlinear dimension reduction algorithm W-map.Wmap model based on Wasserstein distance probability distribution model is proposed to establish similar Wasserstein flows in high dimensional data space and its related low dimensional data space, and the dimension reduction is transformed into the minimum transportation problem. In order to solve the problem of minimizing Wasserstein distance, according to the principle that the Wasserstein flow model of the data is the same as the Wasserstein flow model in the low dimensional space, the most matching low dimensional data projection is found. The experimental results of three groups for different data sets show that W-map can produce high dimensional data reduction visualization results with high correctness and good robustness compared with the traditional probability distribution model.
【作者單位】： 陜西師范大學(xué)物理學(xué)與信息技術(shù)學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(11374199,11574192)~~
【分類號】：O21
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本文編號：2513448