论文标题
二进制分类作为相分离过程
Binary Classification as a Phase Separation Process
论文作者
论文摘要
我们提出了一种称为“相分离二进制分类器（PSBC）”的新二进制分类模型。它由非线性反应扩散方程与普通微分方程的离散化组成，并受到流体行为的启发，即二元流体相相分开的方式。因此，参数和超参数具有物理含义，其效果在几种不同的情况下进行了研究。 PSBC的方程式可以看作是一个动力系统，其系数是可训练的权重，具有与经常性神经网络相似的架构。因此，正向传播等于初始值问题。边界条件也存在，与计算机视觉中的图形技术相似。模型压缩以多种方式利用，重量共享发生在各个层和内部。 该模型是通过经典MNIST数据库的数字成对测试的。相关的多类分类器还使用集合学习，一种与一种技术的组合构建。还显示了如何将PSBC与其他方法（如聚合和PCA）结合在一起，以构建更好的二进制分类器。在数字``0'''和``1''的情况下对边界条件和粘度的作用进行了详尽的研究。
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by fluids behavior, namely, on how binary fluids phase separate. Thus, parameters and hyperparameters have physical meaning, whose effects are studied in several different scenarios. PSBC's equations can be seen as a dynamical system whose coefficients are trainable weights, with a similar architecture to that of a Recurrent Neural Network. As such, forward propagation amounts to an initial value problem. Boundary conditions are also present, bearing similarity with figure padding techniques in Computer Vision. Model compression is exploited in several ways, with weight sharing taking place both across and within layers. The model is tested on pairs of digits of the classical MNIST database. An associated multiclass classifier is also constructed using a combination of Ensemble Learning and one versus one techniques. It is also shown how the PSBC can be combined with other methods - like aggregation and PCA - in order to construct better binary classifiers. The role of boundary conditions and viscosity is thoroughly studied in the case of digits ``0'' and ``1''.
