目录
1.1 fMRI应用：whole-brain fMRI classification
医学图像相关的脑分类数据：fMRI, voxel
- fMRI
fMRI, Funtional magnetic resonance imaging, 功能性磁共振成像
Wikipedia: Functional magnetic resonance imaging or functional MRI (fMRI) measures brain activity by detecting changes associated with blood flow. This technique relies on the fact that cerebral blood flow and neuronal activation are coupled. When an area of the brain is in use, blood flow to that region also increases.
功能磁共振成像或功能MRI（fMRI）通过检测与血流相关的变化来测量大脑活动。 该技术依赖于脑血流和神经元激活相结合的事实。 当使用大脑的某个区域时，流向该区域的血液也会增加。
1.1 fMRI应用：whole-brain fMRI classification
source: Learning Tensor-based Features for whole Brain fMRI Classification, Xiaonan Song, Lingnan Meng, Hong Kong Baptist University
abstract:
Problem: feature extraction methods, e.g. PCA, principal component analysis, have limited usage on whole brain due to the small sample size problem and limited interpretability. => PCA不好
To address: we propose to directly extract features from natural tensor representations(rather than vector) of whole-brain fMRI using mutilinear PCA(MPCA), and map MPCA bases to voxels for interpretability. 多线性PCA从全脑功能磁共振成像中抽取自然张量表示，将MPCA基映射到体素增强可解释性
1) extract low-dimensional tensors by MPCA. 用MPCA抽取低维张量
2) then select a number of MPCA features according to the captured variance or mutual information as the input to SVM. 根据捕获的方差或互信息选择大量MPCA特征作为SVM的输入。
Introduction
problem: whole-brain fMRI have higher exploratory power and lower biasthan ROIs(brain regions of interest), but they are challenging to deal with due to large numbers of voxels. 但是fMRI难以处理大规模的体素，—> whole-brain voxels leading to overfitting, 大规模体素会造成过拟合！！！
method: A critical step for fMRI classification is dimensianality reduction, via feature selection or feature extraction. fMRI分类的关键一步是降维，同于特征选择或特征抽取。
- Feature selection methods, which are popular for fMRI classification, partly due to their good interpreterbility.
approaches: univariate method, mutual information; multivariate method, consider interactions between multiple features.
- Feature extraction methods, MPCA, principle component analysis
problem: PCA making the small sample size problem more severe; a group of PCA seldom interpreted effectively.
method: MPCA, represent multidimensional data as tensorsrather than vectors.
e.g. PCA parameters, 128 x 128 x 64; while MPCA 128 + 128 + 64.
methods: 论文方法
1) Notations and Basic Operations: Our proposed method use the fMRI data represented by the mean percent signal change(PSC) voer the time dimensionas input features and model them directly as third-order tensors(3D data). 使用在时间维度上由平均信号变化百分比表示的fMRI数据作为输入特征，并直接将他们建模位3阶张量(3维数据)
2) MPCA Feature Extraction: we use MPCA to learn multilinear bases from these tensorial input to obtain low-dimensional tensorial MPCA features. 使用mpca从这些张量输入中学习多线性基以获得低维张量mpca特征。
3) MPCA Feature Selection: we then select the most informative MPCA features to form feature vectors for the SVM classifier. 选择信息最丰富的mpca特征组成特征向量以生成svm分类器。
–Therefore, we further perform feature selection based on an importance score using either the variance or the MI criterion.
–We arrange the entries in {Ym}into feature vectors {ym} according to the importance score in descending order. Only the first P entries of {ym} are selected as SVM input.
–We can determine the optimal value for P via cross-validation.
4) Mapping for Interpretability:
we propose a novel scheme to localize discriminating regions by mapping the selected MPCA features to the raw voxel space, with good potential for neuroscience interpretation.
–It is often useful to localize regions in the original voxel space of the brain for interpretation.
–Good features for classification are expected to be closely related to discriminating regions
Therefore, we propose a scheme to map the selected MPCA features (the eigentensors) —> the voxel space. We perform a weighted aggregation of the selected eigentensors first and then determine the Dmost informative voxels to produce a spatial map M by choosing an appropriate threshold T (depending on D): M = Pp=1 wp |Up| > T, where wp is the weight for the pth eigentensor, and | · | denotes the absolute value (magnitude). Note that M is actually a low-rank tensor (rank P) since it is a summation of Prank-one tensors {Up} [8].
- voxel, 体素
体素(voxel)，是体积元素(volumepixel)的简称。一如其名，是数字数据于 三维空间分割上的 最小单位，体素用于三维成像、科学数据与医学影像等领域。
- 张量tensor
向量vector与张量tensor，https://blog.csdn.net/qq_33419476/article/details/115343812
Original: https://blog.csdn.net/qq_33419476/article/details/115593013
Author: 天狼啸月1990
Title: 医学图像～脑分类数据fMRI, voxel
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