CAJ | 학술논문

为了清晰地说明纯度函数失效的原因,首先拓展了纯度函数的定义,得到一种能方便运用数学方法表示的新纯度函数形式,并在其基础上,分析了有些纯度函数在有些情况下会失效,而另外的一些却不会.说明了这种"预测性能"实际上与纯度函数某种特殊的"凹凸性"有关,这种凹凸性只在特定的方向才呈现出来.通过若干定理,阐明了如何通过赫斯矩阵寻找这些特定的方向,而纯度函数的"预测性能"本质上就是该方向性严格凸性质.最后通过若干实验数据,验证了结论.
위료청석지설명순도함수실효적원인,수선탁전료순도함수적정의,득도일충능방편운용수학방법표시적신순도함수형식,병재기기출상,분석료유사순도함수재유사정황하회실효,이령외적일사각불회.설명료저충"예측성능"실제상여순도함수모충특수적"요철성"유관,저충요철성지재특정적방향재정현출래.통과약간정리,천명료여하통과혁사구진심조저사특정적방향,이순도함수적"예측성능"본질상취시해방향성엄격철성질.최후통과약간실험수거,험증료결론.
For the clear explanation for the reason of the failure, the definition of purity functions is expanded to a new one with which the mathematical methods can be conveniently carried. Strict analysis on the reason why some purity functions fail under these circumstances while others are not followed. It is revealed that this kind of "prediction ability" actually stems from a property of being convex in a particular way which appears only in certain directions. With several theorems, a method for finding out these directions through Hessian Matrix is explained. The essence of the prediction ability is actually being strictly convex in certain direction. Finally, experimental results are presented to support the theoretical analysis.