论文标题
更简单的标志优化
Simpler flag optimization
论文作者
论文摘要
我们研究了不同嵌入的旗帜歧管的几何形状，以纳入拉格曼尼亚人的产物中。我们表明，差分几何对象和操作 - 切线矢量，度量，正常矢量，指数图，地球平行，平行传输，梯度，Hessian等）具有封闭形式的分析表达式，可以使用标准数值线性代数进行计算。此外，我们能够在标志歧管中得出与其他梯度下降方法相比表现良好的坐标下降方法。
We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel transport, gradient, Hessian, etc -- have closed-form analytic expressions that are computable with standard numerical linear algebra. Furthermore, we are able to derive a coordinate descent method in the flag manifold that performs well compared to other gradient descent methods.
