網際網路迅速發展與普及化的現代，造就人人都能是內容創作者，從而產生出大量資料，因此有效區分這些大量資料變成了一個重要的問題。而資料探勘即被利用在這問題上，因為資料探勘可以幫助使用者分析大量的資訊，並取得有用的情報。分群是資料探勘裡的一種重要方法，其旨在不使用任何資料標籤的情況下區分資料，使同群內的資料盡可能相似而群之間的資料盡可能不相似。

有很多學者提出使用神經網路來進行區分資料的演算法，其中一種分群的方式為半監督式學習(Semi-Supervised Learning)的演算法，以人工給少量資料標上標籤作為標籤資料集來訓練神經網路，隨後使用訓練後的神經網路來給無標籤的資料標上偽標籤，再同時使用標籤資料集與偽標籤反覆訓練該網路，最終即可用訓練後的網路來區分資料。如果想把這類演算法改成分群演算法的話，則要思考如何在資料標籤移除掉的情況下使用神經網路對資料進行分群。

本研究提出了基於神經網路正切核之譜分群(Spectral Clustering based on Neural Tangent Kernel，SCNTK)來解決上述問題。SCNTK是使用一個無訓練的初始神經網路且過程中無需使用資料標籤的演算法來計算譜分群時所需的相似度矩陣，再對其相似度矩陣進行特徵分解後得出特徵向量，最後將特徵向量透過k-means演算法把各個資料點進行分群。根據實驗結果顯示本研究所提之演算法能有效的解決上述問題，同時與其他近年分群演算法相比有更好的結果。

In the modern age, the internet has gained rapid development and popularization. Because everyone now has the opportunity to become a content creator, a large amount of data has been created. Therefore, distinguishing large amounts of data efficiently becomes an important issue. To provide a solution, data mining is exploited since it has the power to help users analyze enormous amounts of information and extract useful intelligence. Clustering is an important method in data mining, which aims to distinguish data without using any data labels. In clustering, the data in the same cluster should be as similar as possible and the data between different clusters should be as dissimilar as possible.

Many scholars have proposed algorithms to cluster data using neural networks. One of the neural-network-based clustering method is the semi-supervised learning algorithm, which manually labels a small amount of data as a label data set for training. The neural network then utilizes the trained neural network to label unlabeled data with pseudo labels. Afterward, it trains the neural network repeatedly using both the labeled dataset and the pseudo labels. Henceforth, the trained neural network can be used to distinguish data. However, to change these kinds of algorithms into clustering algorithms, it is necessary to consider how to use a neural network to cluster the data when the data labels are removed.

In this study, Spectral Clustering based on Neural Tangent Kernel (SCNTK) is proposed for solving the problems mentioned above. SCNTK is an untrained initial neural network that uses an algorithm without the data labels to calculate the similarity matrix required for clustering. After that, the eigen decomposition of the similarity matrix is carried out. Then the eigenvectors can be obtained, and the eigenvectors are converted into various data forms by using the k-means method. According to the experiment results, the method proposed in this study can effectively solve the problems listed above, and the performance is also better than other recently developed clustering methods.

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