第四章、 實驗
4.2 實驗 B
4.2.1 資料收集與實驗設計
資料的收集方法是在 PDA 上安裝 GPS 座標收集程式，並且走訪各地，
本篇論文實地前往蘭嶼，收集20930 筆資料，分布圖可見圖 4.2-1。收集完的 資料先進行zero-mean 的處理，之後隨機選出其中 80%的資料做為訓練集合，
20%的資料做為測試集合。之後再以本論文提出的方法，分別對東距(TE)和北
距(T )兩個依變數進行迴歸分析，找出東距和北距各別的迴歸公式。 N
(a) 蘭嶼地圖 (b) 實地接收資料
圖 4.2-1 蘭嶼 GPS 資料
小波迴歸的部分，實驗參數如所示表 4.2-1。所選用的母小波為墨西哥帽，
SRGP 的部份參數如表 4.2-2 所示，並採用兩種運算子集合
{
+,-,*,/}
和{
+,-,*,/,sin,cos,pow}
。實驗的輸入則為三維資料，即 GPS 裝置所接收到的經 度(ψ)、緯度(λ)和高度(h)。輸出則為 2-D 平面的東距(TE)和北距(T )兩條迴N 歸公式。表 4.2-1 Wavelet Regression 參數
WR 參數 設定值
母小波 墨西哥帽
a0 2
b0 0.015625 位子取樣 65
伸縮程度 7
門檻值選擇 前三名係數 表 4.2-2 SRGP 參數
SRGP 參數 設定值
停止條件1 Fitness
( )
⋅ ≥1.0停止條件2 Max. Generation = 10000 停止條件3 1000 代 Fitness Value 毫無改進 族群大小 100
突變機率 0.01 最大樹節點各數 1023 適應度比重ω 1 0.7 適應度比重ω 2 0.3
運算子
{
+,-,*,/}
和{
+,-,*,/,sin,cos,pow}
避免結果過於偏頗，相同參數的實驗重複十次。實驗分為三大部分，第一 階段訓練階段(Training Phase)是以隨機挑選出來的 80%資料集合進行迴歸計 算，所找出的公式再進行第二階段的驗證階段(Testing Phase)。將驗證完成的 迴歸公式，用虛擬的路線再次驗證，則是第三階段(Navigation Phase)。
4.2.2 實驗結果
實驗以同樣參數重複十次之後所得到的迴歸結果如圖 4.2-2 所示，實驗平 均後的數據如表 4.2-3 和表 4.2-4 所示。從數據上來看，東距和北距的迴歸誤 差都不大。這是由於蘭嶼本身就是個小島，再加上資料量有2 萬多筆，因此所 得到的迴歸結果精準度非常的高。
表 4.2-3 東距TE結果 Avg Miss Error 0.011625924 Abs AME 0.0567445 MSE 19.24798808 STDEV 3.214468702
表 4.2-4 北距T 結果 N Avg Miss Error 0.00033886 Abs AME 0.002516617 MSE 0.155121984
STDEV 0.2366143
圖 4.2-2 蘭嶼作標轉換迴歸結果
下圖 4.2-3 和圖 4.2-4 是東距和北距對應每一個輸入變數(經度、緯度、高 度)的迴歸結果。
296000 298000 300000 302000 304000 306000 308000 310000
121.48 121.5 121.52 121.54 121.56 121.58
(E) exTree
(a) 經度與東距
296000 298000 300000 302000 304000 306000 308000 310000
22 22.02 22.04 22.06 22.08 22.1
(E) exTree
(b) 緯度與東距
296000 298000 300000 302000 304000 306000 308000 310000
-100 0 100 200 300 400
(E) exTree
(c) 高度與東距 圖 4.2-3 東距迴歸結果
2432000 2434000 2436000 2438000 2440000 2442000 2444000
121.48 121.5 121.52 121.54 121.56 121.58
(N) exTree
(a) 經度與北距
2432000 2434000 2436000 2438000 2440000 2442000 2444000
22 22.02 22.04 22.06 22.08 22.1
(N) exTree
(b) 緯度與北距
2432000 2434000 2436000 2438000 2440000 2442000 2444000
-100 0 100 200 300 400
(N) exTree
實驗的第二階段以 20%的資料進行驗證階段(Testing Phase)，東距迴歸公 式和北距迴歸公式表示在下表所示。
表 4.2-5 驗證階段結果 Avg Miss Error Abs AME 東距 0.003165313 0.218385085 北距 0.066605948 0.144373673
實驗第三階段導航驗證(Navigation Phase)在圖之中。由於蘭嶼外海的部份 並沒有資料點，找出的迴歸公式在外海部分誤差較為高，但也在1.2 以下，而 蘭嶼島之內的導航結果，精準度都在0.3 之內。
圖 4.2-5 導航驗證結果
從導航結果來看，符號式迴歸引擎所找出的座標轉換迴歸公式的確可以代 替傳統的複雜座標轉換公式。實驗結果
第五章、結論與討論
迴歸分析是希望透過數學方式找出資料變數之間的關係。透過迴歸分析可 以解釋變數之間的關聯，也可以藉此預測資料的走向。一對一的簡單迴歸可以 使用數學計算找出精準的迴歸公式，但是一對多的複迴歸是一個非常困難的問 題。透過符號式迴歸可以找出一條迴歸公式，而且這條迴歸公式可以寫成數學 形式，但是符號式迴歸的計算是非常花費時間的運算。
本論文提出結合小波迴歸以及基因規劃兩種技術來增進符號式迴歸引擎 的效能。基因規劃為基礎的符號式迴歸引擎因為演化過程會花費大量時間在尋 找資料趨勢，小波迴歸正好可以解決這問題。透過小波分析出資料的大方向趨 勢，再以逆轉換找到資料趨勢迴歸公式，以此作為基因規劃的初始條件。最後 再用基因規劃的演化找出更精準的迴歸公式。
從實驗結果可以知道，本研究的確可以找到準確的迴歸公式。小波迴歸分 析所得的迴歸公式可以找出資料的趨勢，用此提升基因規劃初始染色體的適應 度，可以讓基因規劃的運算資源集中在尋找更精準的迴歸方程式。 無論是在 人造資料之中或是真實世界中的 GPS 座標轉換的例子之中，都可以得到誤差 值非常低的迴歸公式。
由於小波分析在處理多維度資料時候，其計算量會和資料維度成次方成 長。同時演化式計算中最令人詬病的就是大量的計算時間，因此如何加速小波 分析的處理速度以及縮減基因規劃的演化時間是未來可以研究的方向。
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