基于图上扩散界面方法的多类数据分割
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
摘要：
我们提出了两个基于图的算法高维数据的多类分割。该算法使用的扩散界面模型的基础上的Ginzburg-Landau功能，涉及到总变分压缩传感和图像处理。一个多类的扩展引入使用吉布斯单纯形，与功能的双阱势修改处理多类的情况下。第一个算法最小化的功能使用凸分裂数值方案。第二种算法是使用经典的数值Merriman-Bence-Osher（MBO）方案的图形适应，该方案在扩散和阈值之间交替。我们证明了这两种算法的性能实验上的合成数据，灰度和彩色图像，和几个基准数据集，如MNIST，COIL和WebKB。我们还利用快速数值求解器来寻找图拉普拉斯算子的特征向量和特征值，并利用矩阵的稀疏性。实验结果表明，该算法的分割效果优于或优于现有的多类分割算法。
英文摘要：
We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.
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