眾所周知，神經元網絡內的資訊流是了解大腦如何工作的最重要特徵。大腦研究中研究最多的物種之一是果蠅（Drosophila），它有大約13萬5千條神經元。因此，為了了解信息如何流動以及大腦在特定條件下如何工作，識別神經元的極性無疑是必要且重要的。其中一項重大進展是基於節點的神經元極性標識符(NPIN)的開發，這是一種基於機器學習方法的算法，用於對神經元極性進行高精度預測(Chen-Zhi Su et al. [1]）。

在這些中，我們描述了我們如何將神經元的 3D 光學圖像映射到 2D 級別的樹上，通過適當的修剪去除分支，最後將標準化的數據放入機器程序中進行分類和識別。我們還可以通過偏移或改變修剪層的數量來增加訓練數據，從而為機器學習的訓練過程（即數據增強）產生一個實際上相同但文字不同的神經元。我們的工作將NPIN的準確率從 95% 提高到了 96%。我們還開發了NPIN在社區中的應用網頁（Chen-Zhi Su et al. [1]），推動相關研究在腦科學中的應用。

此外，我們還開發了另一種機器學習模型，用於根據形態識別 FlyCircuit 和 FlyEM 中的神經元。為了確認這樣的數值計算結果，我們還製作了一個網頁，方便生物學家進行註釋，並直接進行比較，以增加ground truth數據。

最後，在研究果蠅大腦中神經元的形態時，我們計算了轉動慣量，用於比較不同的神經元。我們發現所有神經元的數據在轉動慣量的3D空間中都停留在同一個2D平面上，顯示出果蠅大腦中神經元的一個非常特殊的統計特徵。我們的工作顯示了應用機器學習和其他計算方法來研究神經元形態的可能性。

It is known that the information flow within the neuron network is the most important feature to understand how a brain is working. One of the most well-studied species in brain research is fruit fly ($Drosophila$), which has about 135K neurons. Therefore, it is certainly necessary and important to identify the axon-dendrite polarity of neurons in order to understand how the information flows and how a brain works under a certain condition. One of the major progress is the development of Node-based Polarity Identifier of Neurons (NPIN), which is an algorithm based on machine learning methods for a high precision prediction of neuron polarity(Chen-Zhi Su et al. [1]).

In this these, we describe how we map the 3D optical images of neurons onto 2D level trees, remove branches by appropriate pruning, and then finally put the standardized data into the machine program for classification and recognition. We could also increase the training data by offsetting or changing the number of pruning layers, leading to an effectively identical but literately different neurons for the training process of machine learning, i.e data augmentation. Our work improve the accuracy of NPIN from 95\% to 96\%. We also have developed a web page for the application of NPIN to the community (Chen-Zhi Su et al. [1]), promoting related research for its application in brain science.

Besides, we developed another machine learning model to identify neurons in FlyCircuit and FlyEM based on their morphology. In order to confirm such numerical calculation result, we also made a web page to facilitate the annotation for biologists and carried out such comparison directly for the increase of ground truth data.

Finally, when investigating the morphology of neurons in Drosophila brain, we calculated the moment of inertial for the comparison of different neurons. We find that data of all neurons stay in the same 2D plane in the 3D space of moment of inertial, showing a very special statistical feature of neurons in Drosophila brain. Our work shows the possibility to apply machine learning and other computational methods to investigate the morphology of neurons.

Contents
1 Introduction 1
1.1 Dataset:FlyCircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Dataset:FlyEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Method 7
2.1 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 NPIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Augmentation in Identification of FlyCircuit Polarity 14
3.1 Vibration for Augmentation . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Reduce tree for Augmentation . . . . . . . . . . . . . . . . . . . . . 17
4 Analysis of FlyEM 22
4.1 Reduce Tree for FlyEM data . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Identification of FlyEM Polarity . . . . . . . . . . . . . . . . . . . . 22
5 Mapping of FlyCircuit and FlyEM 25
5.1 FC-Like Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2 Website of Mapping Label Work . . . . . . . . . . . . . . . . . . . . 28
6 Moment of inertia of Neurons 34
7 Conclusions 41

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