线性判别式分析(Linear Discriminant Analysis),简称为LDA。也称为Fisher线性判别(Fisher Linear Discriminant,FLD),是模式识别的经典算法,在1996年由Belhumeur引入模式识别和人工智能领域。
基本思想是将高维的模式样本投影到最佳鉴别矢量空间,以达到抽取分类信息和压缩特征空间维数的效果,投影后保证模式样本在新的子空间有最大的类间距离和最小的类内距离,即模式在该空间中有最佳的可分离性。

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Neurodegenerative parkinsonism can be assessed by dopamine transporter single photon emission computed tomography (DaT-SPECT). Although generating images is time consuming, these images can show interobserver variability and they have been visually interpreted by nuclear medicine physicians to date. Accordingly, this study aims to provide an automatic and robust method based on Diffusion Maps and machine learning classifiers to classify the SPECT images into two types, namely Normal and Abnormal DaT-SPECT image groups. In the proposed method, the 3D images of N patients are mapped to an N by N pairwise distance matrix and are visualized in Diffusion Maps coordinates. The images of the training set are embedded into a low-dimensional space by using diffusion maps. Moreover, we use Nystr\"om's out-of-sample extension, which embeds new sample points as the testing set in the reduced space. Testing samples in the embedded space are then classified into two types through the ensemble classifier with Linear Discriminant Analysis (LDA) and voting procedure through twenty-five-fold cross-validation results. The feasibility of the method is demonstrated via Parkinsonism Progression Markers Initiative (PPMI) dataset of 1097 subjects and a clinical cohort from Kaohsiung Chang Gung Memorial Hospital (KCGMH-TW) of 630 patients. We compare performances using Diffusion Maps with those of three alternative manifold methods for dimension reduction, namely Locally Linear Embedding (LLE), Isomorphic Mapping Algorithm (Isomap), and Kernel Principal Component Analysis (Kernel PCA). We also compare results using 2D and 3D CNN methods. The diffusion maps method has an average accuracy of 98% for the PPMI and 90% for the KCGMH-TW dataset with twenty-five fold cross-validation results. It outperforms the other three methods concerning the overall accuracy and the robustness in the training and testing samples.

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Neurodegenerative parkinsonism can be assessed by dopamine transporter single photon emission computed tomography (DaT-SPECT). Although generating images is time consuming, these images can show interobserver variability and they have been visually interpreted by nuclear medicine physicians to date. Accordingly, this study aims to provide an automatic and robust method based on Diffusion Maps and machine learning classifiers to classify the SPECT images into two types, namely Normal and Abnormal DaT-SPECT image groups. In the proposed method, the 3D images of N patients are mapped to an N by N pairwise distance matrix and are visualized in Diffusion Maps coordinates. The images of the training set are embedded into a low-dimensional space by using diffusion maps. Moreover, we use Nystr\"om's out-of-sample extension, which embeds new sample points as the testing set in the reduced space. Testing samples in the embedded space are then classified into two types through the ensemble classifier with Linear Discriminant Analysis (LDA) and voting procedure through twenty-five-fold cross-validation results. The feasibility of the method is demonstrated via Parkinsonism Progression Markers Initiative (PPMI) dataset of 1097 subjects and a clinical cohort from Kaohsiung Chang Gung Memorial Hospital (KCGMH-TW) of 630 patients. We compare performances using Diffusion Maps with those of three alternative manifold methods for dimension reduction, namely Locally Linear Embedding (LLE), Isomorphic Mapping Algorithm (Isomap), and Kernel Principal Component Analysis (Kernel PCA). We also compare results using 2D and 3D CNN methods. The diffusion maps method has an average accuracy of 98% for the PPMI and 90% for the KCGMH-TW dataset with twenty-five fold cross-validation results. It outperforms the other three methods concerning the overall accuracy and the robustness in the training and testing samples.

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