Learning Strictly Orthogonal p-Order Nonnegative Laplacian Embedding via Smoothed Iterative Reweighted Method
Learning Strictly Orthogonal p-Order Nonnegative Laplacian Embedding via Smoothed Iterative Reweighted Method
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DOI：
10.24963/ijcai.2019/561
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
Haoxuan Yang;Kai Liu;Hua Wang;F. Nie
中科院分区：
文献类型：
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作者：
Haoxuan Yang;Kai Liu;Hua Wang;F. Nie
拉普拉斯嵌入 (LE) 是一种利用图揭示高维数据内在几何结构的强大方法。事实证明，对 LE 目标施加正交和非负约束可以有效避免简并和负解，但同时实现这些解具有挑战性，因为它们是非线性和非凸的。此外，最近的研究表明，在 LE 中使用 L2 范数距离的 p 阶可以找到聚类的最佳解决方案，并提高嵌入模型对异常值的鲁棒性，尽管这使得优化目标变得不光滑并且通常难以有效求解。在这项工作中，我们研究使用 L2 范数距离的 p 阶并满足正交和非负约束的 LE。我们引入了一种新颖的平滑迭代重加权方法来解决这个具有挑战性的优化问题并严格分析其收敛性。我们通过对合成数据集和真实数据集的广泛实证研究证明了我们提出的方法的有效性和潜力。
Laplacian Embedding (LE) is a powerful method to reveal the intrinsic geometry of high-dimensional data by using graphs. Imposing the orthogonal and nonnegative constraints onto the LE objective has proved to be effective to avoid degenerate and negative solutions, which, though, are challenging to achieve simultaneously because they are nonlinear and nonconvex. In addition, recent studies have shown that using the p-th order of the L2-norm distances in LE can find the best solution for clustering and promote the robustness of the embedding model against outliers, although this makes the optimization objective nonsmooth and difficult to efficiently solve in general. In this work, we study LE that uses the p-th order of the L2-norm distances and satisfies both orthogonal and nonnegative constraints. We introduce a novel smoothed iterative reweighted method to tackle this challenging optimization problem and rigorously analyze its convergence. We demonstrate the effectiveness and potential of our proposed method by extensive empirical studies on both synthetic and real data sets.