目錄

1. fMRI

1.1 fMRI應用：whole-brain fMRI classification

2. voxel, 體素

3. 張量tensor

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醫學圖像相關的腦分類數據：fMRI, voxel

1. 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）通過檢測與血流相關的變化來測量大腦活動。 該技術依賴于腦血流和神經元激活相結合的事實。 當使用大腦的某個區域時，流向該區域的血液也會增加。

1.1 fMRI應用：whole-brain fMRI classification

source: Learning Tensor-based Features for whole Brain fMRI Classification,?Xiaonan Song, Lingnan Meng, Hong Kong Baptist University

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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. 多線性PCA從全腦功能磁共振成像中抽取自然張量表示，將MPCA基映射到體素增強可解釋性

? ? ?1) extract low-dimensional tensors by MPCA. 用MPCA抽取低維張量

? ? ?2) then select a number of MPCA features according to the captured variance or mutual information as the input to SVM. 根據捕獲的方差或互信息選擇大量MPCA特征作為SVM的輸入。

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Introduction

problem: whole-brain?fMRI have higher exploratory power and lower bias than ROIs(brain regions of interest), but?they are challenging to deal with due to large numbers of voxels. 但是fMRI難以處理大規模的體素，---> whole-brain voxels leading to overfitting, 大規模體素會造成過擬合！！！

method: A critical step for fMRI classification is dimensianality reduction, via feature selection or feature extraction. fMRI分類的關鍵一步是降維，同于特征選擇或特征抽取。

• 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 tensors rather than vectors.

? ? e.g. PCA parameters, 128 x 128 x 64; while MPCA 128 + 128 + 64.

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methods: 論文方法?

1)?Notations and Basic Operations:?Our proposed method use the fMRI data represented by the mean percent signal change(PSC) voer the time dimension as input features and model them directly as third-order tensors(3D data). 使用在時間維度上由平均信號變化百分比表示的fMRI數據作為輸入特征，并直接將他們建模位3階張量(3維數據)

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從這些張量輸入中學習多線性基以獲得低維張量mpca特征。

3) MPCA Feature Selection:?we then select the most informative MPCA features to form feature vectors for the SVM classifier. 選擇信息最豐富的mpca特征組成特征向量以生成svm分類器。

? --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].

2. voxel, 體素

體素(voxel)，是體積元素(volumepixel)的簡稱。一如其名，是數字數據于三維空間分割上的最小單位，體素用于三維成像、科學數據與醫學影像等領域。

3. 張量tensor

向量vector與張量tensor，https://blog.csdn.net/qq_33419476/article/details/115343812

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