论文标题
二元分类的基本定律
Fundamental Laws of Binary Classification
论文作者
论文摘要
找到最小风险二进制分类系统的判别功能是一个新的几何基因座问题，它需要解决二进制分类的基本基因座方程系统 - 遵守深层统计法。 We show that a discriminant function of a minimum risk binary classification system is the solution of a locus equation that represents the geometric locus of the decision boundary of the system, wherein the discriminant function is connected to the decision boundary by an exclusive principal eigen-coordinate system -- at which point the discriminant function is represented by a geometric locus of a novel principal eigenaxis -- structured as a dual locus of likelihood组件和主要特征力组件。我们证明，最低风险二进制分类系统通过定位平衡点可以共同最大程度地减少其特征和风险，在这一点上，该系统表现出的临界最小征素能对称地集中在系统中，以使系统的新型原理表现出对对称性和对称性的影响，从而反对构造和相反的势力，从而对其进行了反对，并具有相对的势力和量化的影响。彼此之间 - 关于新型主要特征力的几何中心，其中系统的统计支点是。因此，最小风险二进制分类系统满足统计平衡状态 - 因此，在系统的决策空间内，共同将允许的特征和预期风险共同最小化 - 在这一点上，该系统表现出最低分类误差的可能性。
Finding discriminant functions of minimum risk binary classification systems is a novel geometric locus problem -- which requires solving a system of fundamental locus equations of binary classification -- subject to deep-seated statistical laws. We show that a discriminant function of a minimum risk binary classification system is the solution of a locus equation that represents the geometric locus of the decision boundary of the system, wherein the discriminant function is connected to the decision boundary by an exclusive principal eigen-coordinate system -- at which point the discriminant function is represented by a geometric locus of a novel principal eigenaxis -- structured as a dual locus of likelihood components and principal eigenaxis components. We demonstrate that a minimum risk binary classification system acts to jointly minimize its eigenenergy and risk by locating a point of equilibrium, at which point critical minimum eigenenergies exhibited by the system are symmetrically concentrated in such a manner that the novel principal eigenaxis of the system exhibits symmetrical dimensions and densities, so that counteracting and opposing forces and influences of the system are symmetrically balanced with each other -- about the geometric center of the locus of the novel principal eigenaxis -- whereon the statistical fulcrum of the system is located. Thereby, a minimum risk binary classification system satisfies a state of statistical equilibrium -- so that the total allowed eigenenergy and the expected risk exhibited by the system are jointly minimized within the decision space of the system -- at which point the system exhibits the minimum probability of classification error.
