论文标题
使用参考矢量和通过增长神经气体产生的网络的拓扑结构的近似光谱聚类
Approximate spectral clustering using both reference vectors and topology of the network generated by growing neural gas
论文作者
论文摘要
光谱聚类（SC）是最受欢迎的聚类方法之一，通常优于传统聚类方法。 SC使用从数据集的相似性矩阵中计算出的拉普拉斯矩阵的特征向量。 SC具有严重的缺点：从特征向量的计算和存储空间复杂性来存储相似性矩阵的时间复杂性的显着增加。为了解决这些问题，我使用生长的神经气（GNG）产生的网络开发了新的近似光谱聚类，该网络在本研究中称为ASC带有GNG。带有GNG的ASC不仅使用参考向量进行向量量化，还使用网络的拓扑来提取数据集中数据点之间拓扑关系。使用GNG的ASC计算GNG产生的参考矢量和网络拓扑的相似性矩阵。使用GNG从数据集生成的网络，带有GNG的ASC可以减少计算和空间复杂性并提高聚类质量。在这项研究中，我证明具有GNG的ASC可以有效地减少计算时间。此外，这项研究表明，具有GNG的ASC提供了等于或更好的聚类性能。
Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious drawbacks: the significant increases in the time complexity derived from the computation of eigenvectors and the memory space complexity to store the similarity matrix. To address the issues, I develop a new approximate spectral clustering using the network generated by growing neural gas (GNG), called ASC with GNG in this study. ASC with GNG uses not only reference vectors for vector quantization but also the topology of the network for extraction of the topological relationship between data points in a dataset. ASC with GNG calculates the similarity matrix from both the reference vectors and the topology of the network generated by GNG. Using the network generated from a dataset by GNG, ASC with GNG achieves to reduce the computational and space complexities and improve clustering quality. In this study, I demonstrate that ASC with GNG effectively reduces the computational time. Moreover, this study shows that ASC with GNG provides equal to or better clustering performance than SC.
