摘要：

局部保持投影(LPP)方法是机器学习领域中一种经典的降维方法。然而LPP方法以及部分改进方法在构建数据的局部结构时简单地使用k最近邻(k-NN)分类算法寻找样本的近邻点, 容易受到参数k、噪声和异常值的影响。为了解决上述问题, 提出一种基于最优近邻的LPP方法。该方法使用寻找最优近邻算法, 在找到样本近邻点后, 进一步选择与样本有一定数量的共同近邻点的近邻样本作为最优近邻, 通过共同近邻点的限定来选择与样本最相似的近邻, 增强近邻样本间的相关性, 避免了传统LPP方法受参数k影响大等问题。在选择出足够的样本最优近邻后, 构建数据局部结构, 以便准确地反映数据的本质结构特征, 使降维后的数据能最大程度保留样本的有效信息, 提升后续机器学习模型的性能。公共图像数据集上的对比实验结果表明, 该方法具有较好的数据降维效果, 有效地提高了图像识别准确率。

关键词: 局部保持投影方法, 最优近邻, 近邻样本, 降维, 特征提取

Abstract:

Locality Preserving Projection(LPP) is a classical dimensionality reduction method used in machine learning. However, the LPP method and some improved methods simply use the k-Nearest Neighbor(k-NN) classification algorithm to find the nearest neighbors of the samples when constructing the local structure of the data, which is easily affected by the parameter k, noise, and outliers. To solve the above problems, a LPP projection method based on the optimal nearest neighbor algorithm is proposed. The proposed method employs the optimal nearest neighbor algorithm to find the sample nearest neighbor points. Then, the algorithm further selects the nearest neighbor samples with a certain number of common points as the optimal nearest neighbors. Then, the algorithm selects the nearest neighbors that are most similar to the samples by limiting the common nearest neighbor points, thereby enhancing the correlation between the nearest neighbor samples. This selection circumvents the problem of the traditional LPP method being greatly influenced by the parameter k. After selecting sufficient sample optimal nearest neighbors, the local structure of the data is constructed to accurately reflect the essential structural features of the data such that dimensionality reduction can retain the effective information of the samples to the maximum extent and improve the performance of the subsequent machine learning models. Comparative experimental results obtained using a public image dataset show that the proposed method has a good data dimensionality reduction effect and effectively improves image recognition accuracy.

Key words: Local Preserving Projection(LPP) method, optimal nearest neighbor, nearest neighbor sample, dimensionality reduction, feature extraction