智能系统学报
智能繫統學報
지능계통학보
CAAI TRANSACTIONS ON INTELLIGENT SYSTEMS
2013年
3期
266-270
,共5页
支持向量回归机%多项式光滑函数%逼近精度%对称函数
支持嚮量迴歸機%多項式光滑函數%逼近精度%對稱函數
지지향량회귀궤%다항식광활함수%핍근정도%대칭함수
support vector regression%polynomial smoothing function%approximation accuracies%symmetric function
为了解决支持向量回归机多项式光滑函数的逼近精度问题，根据该类光滑函数的复杂性，提出五步求的基本思路：首先把多项式光滑函数的逼近精度问题表示为一个求逼近函数的最大值问题，接着证明这个逼近函数是一个对称函数，然后分别求出逼近函数在[0，ε]和（ε，＋ゥ）上的最大值，最后对这2个最大值进行比较，得出光滑函数的逼近精度。通过实例计算，结果证明了该方法的有效性和正确性，解决了无穷多个多项式光滑函数的逼近精度问题，为光滑支持向量回归机提供了基本的理论支持。
為瞭解決支持嚮量迴歸機多項式光滑函數的逼近精度問題，根據該類光滑函數的複雜性，提齣五步求的基本思路：首先把多項式光滑函數的逼近精度問題錶示為一箇求逼近函數的最大值問題，接著證明這箇逼近函數是一箇對稱函數，然後分彆求齣逼近函數在[0，ε]和（ε，＋ゥ）上的最大值，最後對這2箇最大值進行比較，得齣光滑函數的逼近精度。通過實例計算，結果證明瞭該方法的有效性和正確性，解決瞭無窮多箇多項式光滑函數的逼近精度問題，為光滑支持嚮量迴歸機提供瞭基本的理論支持。
위료해결지지향량회귀궤다항식광활함수적핍근정도문제，근거해류광활함수적복잡성，제출오보구적기본사로：수선파다항식광활함수적핍근정도문제표시위일개구핍근함수적최대치문제，접착증명저개핍근함수시일개대칭함수，연후분별구출핍근함수재[0，ε]화（ε，＋ゥ）상적최대치，최후대저2개최대치진행비교，득출광활함수적핍근정도。통과실례계산，결과증명료해방법적유효성화정학성，해결료무궁다개다항식광활함수적핍근정도문제，위광활지지향량회귀궤제공료기본적이론지지。
In order to solve the problem of polynomial smoothing function ’ s approximation accuracies for support vector regression, the researcher proposes to solve the problem utilizing a five step approach , according to the com-plexity of smooth functions.The first step, examines the problem of the approximation accuracy in the polynomial smoothing function represented by solving the maximum value of an approximation function ; second, the function was verified to be a symmetric function;third, the maximum values of the approximation function were derived re-spectively at the intervals [0,ε] and (ε,+ゥ);fourth, the two maximum values were compared, and finally the approximation accuracy was obtained .Through the calculation with examples, the correctness and effectiveness of the method was validated, and the approximation accuracy problem of the infinite polynomial smoothing functions was systematically solved in this paper , which offers basic theoretical support for smooth support vector regression .
