论文标题
机器学习中Legendre分解的实验分析
Experimental Analysis of Legendre Decomposition in Machine Learning
论文作者
论文摘要
在这份技术报告中，我们分析了Legendre分解理论和应用中非负张量的分解。从理论上讲，综述了Legendre分解中双参数和双重歧管的属性，并分析了张量投影和参数更新的过程。在应用中，进行了一系列的验证实验和群集实验，该实验在子曼群上进行了参数，希望找到有效的输入张量的有效的较低维表示。实验结果表明，子曼群上的参数无法直接用作低级表示。结合分析，我们将Legendre的分解与神经网络和低级表示应用联系起来，并提出了一些有希望的前景。
In this technical report, we analyze Legendre decomposition for non-negative tensor in theory and application. In theory, the properties of dual parameters and dually flat manifold in Legendre decomposition are reviewed, and the process of tensor projection and parameter updating is analyzed. In application, a series of verification experiments and clustering experiments with parameters on submanifold were carried out, hoping to find an effective lower dimensional representation of the input tensor. The experimental results show that the parameters on submanifold have no ability to be directly used as low-rank representations. Combined with analysis, we connect Legendre decomposition with neural networks and low-rank representation applications, and put forward some promising prospects.
