论文标题
信噪比和带宽对高维嘈杂点云的图形拉普拉斯频谱的影响
Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud
论文作者
论文摘要
我们系统地研究了基于核的图形laplacian（GL）的光谱，该图在非null设置中由高维和嘈杂的随机点云构成。当从嵌入在低维欧几里得子空间中的歧管中采样清洁信号时，该模型是通过研究模型来动机的，并因高维噪声而损坏。我们量化了信号和噪声在信噪比（SNR）不同区域的相互作用，并报告GL的奇特光谱行为。此外，我们探讨了所选内核带宽对SNR不同区域的GL光谱的影响，这导致了内核带宽的自适应选择，这与实际数据中的共同实践一致。该结果为对从业者如何应用GL的理论理解铺平了道路。
We systematically study the spectrum of kernel-based graph Laplacian (GL) constructed from high-dimensional and noisy random point cloud in the nonnull setup. The problem is motived by studying the model when the clean signal is sampled from a manifold that is embedded in a low-dimensional Euclidean subspace, and corrupted by high-dimensional noise. We quantify how the signal and noise interact over different regions of signal-to-noise ratio (SNR), and report the resulting peculiar spectral behavior of GL. In addition, we explore the impact of chosen kernel bandwidth on the spectrum of GL over different regions of SNR, which lead to an adaptive choice of kernel bandwidth that coincides with the common practice in real data. This result paves the way to a theoretical understanding of how practitioners apply GL when the dataset is noisy.
