A multivariate regression model of affine and diffeomorphic transformation sequences - FineMorphs - is presented. Leveraging concepts from shape analysis, model states are optimally "reshaped" by diffeomorphisms generated by smooth vector fields during learning. Affine transformations and vector fields are optimized within an optimal control setting, and the model can naturally reduce (or increase) dimensionality and adapt to large datasets via suboptimal vector fields. An existence proof of solution and necessary conditions for optimality for the model are derived. Experimental results on real datasets from the UCI repository are presented, with favorable results in comparison with state-of-the-art in the literature and densely-connected neural networks in TensorFlow.

翻译：本文提出了一种仿射与微分同胚变换序列的多元回归模型——FineMorphs。该模型借鉴形状分析中的概念，在训练过程中通过光滑向量场生成的微分同胚对模型状态进行最优"重塑"。仿射变换与向量场在最优控制框架下进行优化，且模型能够自然地降维（或升维），并借助次优向量场适应大规模数据集。本文推导了该模型解的存在性证明及最优性必要条件。在UCI数据库真实数据集上的实验结果显示，该模型与现有文献中的最先进方法及TensorFlow中密集连接神经网络相比均取得了更优表现。