高維資料的變數選擇

Abstract

變數選擇被定義為刪除那些沒有資訊活重複的變數，而後從所有變數中挑選子集出來的一個過程。它可以看作一種搜尋的問題，對每一個變數決定是否為可能的子集變數。變數選擇的目標是用較少的變數去做預測。在這篇文章的目的是解決高維度的資料的問題，所以想要去找出各種可能的子集再加以量測是不太可能的，所以我們以量測變數來代替量測子集。這種方法叫變數分級。我們用來選擇變數的方法是PCA､ ANOVA及Classification Tree。變數分級的方法可以非常快速的選擇變數。我們發現我們所用的方法在線性資料中比挑子集的方法更為快速，且當有overfitting的問題產生時，ANOVA和Classification Tree顯得非常有效去解決這個問題。我們的方法在不同的資料有不同的表現，其他種類的資料或更有效的方法在未來的工作中是值得研究的。

Variable selection is defined as the process of choosing a subset of the original predictive variables by eliminating redundant variables and those with little or no predictive information. It can be viewed as a search problem, with each state in the search space specifying a subset of the possible variables. The goal of variable selection is to use less variables to predict class. The objective in this paper is to solve the problem of high-dimensional data sets, and it is nearly impossible to measure the score of each subset, so we measure the importance score of each variable instead of measure the score of each subset. This is called Variable Ranking. We use the methods of PCA, ANOVA, and Classification Tree to select variables. The methods of variable ranking are fast in selecting variable. We found that our methods of variable ranking are more useful and faster than minimum subset selection in linear data and when an overfitting problem occur, ANOVA and CT can solve the problem by deleting irrelevant variables. Since our methods have different performance in different data sets, the other kinds of data sets are worth studying in the future work.