發展一超方體法以求知物件的分類規則

Abstract

超平面法(Hyper-Plane Methods)及超球體法(Hyper-Sphere Methods)是常 見的分類法。超平面法計算便利但不適用於非線性的分類環境；而超球體法雖可 用於非線性環境但計算困難。本研究擬發展一超方體法(Hyper-Cube Method)使 便於計算又適合於非線性環境。基於給定的分類資料，超方體法可將不同物件加 以區隔至各類的方體空間，經由相關方體的聯集運算後，推導出物件分類的規 則。本研究預期所提出的規則在準確度、涵蓋度及精簡度上優於目前常用的分類 法。本研究將應用超方體法於檢測實際的生物醫學資料、台灣電子公司財務資料 (2002-2011)及IMD 世界競爭力資料，以佐證超方體法的實用性。 本研究計畫為期二年。第一年著重於回顧分類問題的現有方法，第二年提出 進階超方體方法的理論並設計相關的演算法並用於求解各類型大尺度的管理議 題等分類法問題。

Hyper-plane methods and Hyper-sphere methods are commonly used techniques in classifying objects. A Hyper-plane method is efficient in computing but hard to fit nonlinear situation; on the contrary, a Hyper-sphere method has better fitness for nonlinearity but hard to compute. This project proposes an innovative method, called Hyper-Cube Method (HCM), to classify objects effectively under nonlinear environment. Given a set of objects with some classes, HCM separates the objects into different cubes, where each cube is assigned to a class. Via the union of these cubes, we utilize mixed integer programs to induce classification rules with better rates of accuracy, support and compactness. Various practical data sets including benchmark biological and medicine data sets, financial data set of Taiwan electronic companies (2002~ 2011), and a data set of world competitiveness of IMD (2002-2010) are tested to illustrate the advantages of HCM over current methods such as Decision tree methods, hyper-plan methods, and Hyper-sphere methods. This research project will last for two years. The first year is put on reviewing current methods about classification then to develop theoretical propositions of optimal methods. The second year is to design an effective Hyper-Cube algorithm and classify large scale multiple scaling data using HCM to compare its effectiveness with current classification methods.