基于相对距离的拉普拉斯特征映射

G. Zhong, Xinwen Hou, Cheng-Lin Liu
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引用次数: 2

摘要

在模式识别和机器学习的许多领域中,低维数据通常嵌入在高维空间中。为了从高维数据中发现低维表示,已有许多降维和流形学习方法。基于局部性的流形学习方法通常依赖于相邻点之间的距离度量。本文提出了一种新的距离度量,称为相对距离,它是从数据中学习来的,可以更好地反映相对密度。将相对距离与拉普拉斯特征映射(LE)相结合,得到了一种基于相对距离的拉普拉斯特征映射(RDLE)非线性降维算法。基于相对距离的两种不同定义,给出了相对距离的两种变化。为了有效地投影样本外数据,我们还提出了线性版本的RDLE, LRDLE。玩具问题和实际数据的实验结果证明了我们的方法的有效性。
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Relative Distance-Based Laplacian Eigenmaps
In many areas of pattern recognition and machine learning, low dimensional data are often embedded in a high dimensional space. There have been many dimensionality reduction and manifold learning methods to discover the low dimensional representation from high dimensional data. Locality based manifold learning methods often rely on a distance metric between neighboring points. In this paper, we propose a new distance metric named relative distance, which is learned from the data and can better reflect the relative density. Combining the relative distance with Laplacian Eigenmaps (LE), we obtain a new algorithm called Relative Distance-based Laplacian Eigenmaps (RDLE) for nonlinear dimensionality reduction. Based on two different definitions of the relative distance, we give two variations of the RDLE. For efficient projection of out-of-sample data, we also present the linear version of RDLE, LRDLE. Experimental results on toy problems and real-world data demonstrate the effectiveness of our methods.
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