We present Tangent Space Belief Propagation (TSBP) as a method for graph denoising to improve the robustness of manifold learning algorithms. Dimension reduction by manifold learning relies heavily on the accurate selection of nearest neighbors, which has proven an open problem for sparse and noisy datasets. TSBP uses global nonparametric belief propagation to accurately estimate the tangent spaces of the underlying manifold at each data point. Edges of the neighborhood graph that deviate from the tangent spaces are then removed. The resulting denoised graph can then be embedded into a lower-dimensional space using methods from existing manifold learning algorithms. Artificially generated manifold data, simulated sensor data from a mobile robot, and high dimensional tactile sensory data are used to demonstrate the efficacy of our TSBP method.

中文翻译：

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TSBP：流形学习的切线空间信念传播

我们将切线空间置信度传播 (TSBP) 作为一种图去噪方法，以提高流形学习算法的鲁棒性。流形学习的降维在很大程度上依赖于最近邻居的准确选择，这已被证明是稀疏和嘈杂数据集的一个开放问题。TSBP 使用全局非参数置信传播来准确估计每个数据点的基础流形的切线空间。然后去除偏离切线空间的邻域图的边。然后可以使用现有流形学习算法中的方法将得到的去噪图嵌入到低维空间中。人工生成的流形数据、来自移动机器人的模拟传感器数据和高维触觉传感器数据用于证明我们的 TSBP 方法的有效性。