EigenGame：作为纳什均衡的PCA
EigenGame: PCA as a Nash Equilibrium
摘要：
我们提出了一个新的观点，主成分分析（PCA）作为一个竞争性的游戏中，每个近似的特征向量是由一个球员，其目标是最大化自己的效用函数控制。我们分析了这个PCA游戏的属性及其基于梯度的更新行为。由此产生的算法--它将Oja规则中的元素与广义Gram-Schmidt正交化相结合--自然是分散的，因此可以通过消息传递并行化。我们证明了该算法的可扩展性与实验上的大型图像数据集和神经网络激活。我们将讨论如何将PCA作为一个可微游戏的新观点，可以导致进一步的算法发展和见解。
英文摘要：
We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA game and the behavior of its gradient based updates. The resulting algorithm -- which combines elements from Oja's rule with a generalized Gram-Schmidt orthogonalization -- is naturally decentralized and hence parallelizable through message passing. We demonstrate the scalability of the algorithm with experiments on large image datasets and neural network activations. We discuss how this new view of PCA as a differentiable game can lead to further algorithmic developments and insights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
