實現樸素貝葉斯分類器，並且根據李航《統計機器學習》第四章提供的資料訓練與測試，結果與書中一致

分別實現了樸素貝葉斯以及帶有laplace平滑的樸素貝葉斯

%書中例題實現樸素貝葉斯
%特徵1的取值集合
A1=[1;2;3];
%特徵2的取值集合
A2=[4;5;6];%S M L
AValues={A1;A2};
%Y的取值集合
YValue=[-1;1];
%資料集和
T=[ 1,4,-1;
    1,5,-1;
    1,5,1;
    1,4,1;
    1,4,-1;
    2,4,-1;
    2,5,-1;
    2,5,1;
    2,6,1;
    2,6,1;
    3,6,1;
    3,5,1;
    3,5,1;
    3,6,1;
    3,6,-1];
%訓練帶Laplace平滑的樸素貝葉斯模型
ltheta = LaplaceNBtrain(T(:, 1:size(T, 2) - 1), T(:, size(T, 2)), AValues, YValue, 1);
%訓練樸素貝葉斯模型
theta = NBtrain(T(:, 1:size(T, 2) - 1), T(:, size(T, 2)), AValues, YValue);
%測試兩個資料與書中答案相符
ans = NBtest(theta, [2,4;], AValues, YValue)
lans = NBtest(ltheta, [2,4;], AValues, YValue)

function y = NBtest(theta, X, AValues, YValue)
    Xindice=ones(size(X, 1), size(X, 2));
    %找到特徵在取值集合中的下標,將X矩陣轉化為下標矩陣
    for j=1:1:size(X, 2)
        AXi = AValues{j, 1};
        for i=1:1:size(X, 1)
            for t=1:1:size(AXi, 1)
                if(X(i, j) == AXi(t, 1))
                    Xindice(i, j) = t;
                    break
                end
            end
        end
    end
    %矩陣用於記錄所有X在不同Yi下的P(X|Y)P(Y)
    Ys = zeros(size(X, 1), size(YValue, 1));
    PX_Y = theta{1,1};
    PY = theta{2,1};
    for i=1:1:size(Ys, 1)
        x=Xindice(i, :);
        for k=1:1:size(Ys, 2)
            ans = PY(k, 1);
            for j=1:1:size(x, 2)
                ans = ans * PX_Y{k, j}(x(1, j), 1);
            end
            Ys(i, k) = ans;
        end
    end
    Ys
    %後驗概率最大化
    y=zeros(size(Ys, 1), 1);
    for i=1:1:size(Ys, 1)
        max = -1;
        max_indice = 0;
        for j=1:1:size(Ys, 2)
            if(Ys(i, j) > max)
                max = Ys(i, j);
                max_indice = j;
            end
        end
        y(i, 1) = YValue(max_indice, 1);
    end
end

function theta=NBtrain(X,Y,AValues,YValue)
    %計算先驗概率
    TY = zeros(size(YValue, 1), 1);
    for i=1:1:size(Y, 1)
        for j=1:1:size(YValue)
            if(Y(i, 1) == YValue(j, 1))
                Y(i,1);
                TY(j, 1) = TY(j, 1) + 1;
                break
            end
        end
    end
    PY = TY/size(Y, 1);
    %計算條件概率
    pX_Y=cell(size(YValue, 1), size(X, 2));
    for k=1:1:size(YValue, 1)
        %條件y＝yk
        for i=1:1:size(X, 2)
            %i為特徵編號
            %取得第i個特徵的取值集合
            XAi = AValues{i, 1};
            TXij_Y = zeros(size(XAi, 1), 1);
            for j=1:1:size(XAi, 1)
                %查詢資料中所有Y＝yk且特徵i的值為Aij的資料個數並累加
                for t=1:1:size(X, 1)
                    if(Y(t, 1)==YValue(k, 1) && X(t, i) == XAi(j, 1))
                        TXij_Y(j, 1) = TXij_Y(j, 1) + 1;
                    end
                end
            end
            PX_Y{k, i} = TXij_Y/TY(k, 1);
        end
    end
    theta = cell(2,1);
    theta{1,1} = PX_Y;
    theta{2,1} = PY;
end

function theta=LaplaceNBtrain(X,Y,AValues,YValue,lambda)
    %計算先驗概率
    TY = zeros(size(YValue, 1), 1);
    for i=1:1:size(Y, 1)
        for j=1:1:size(YValue)
            if(Y(i, 1) == YValue(j, 1))
                Y(i,1);
                TY(j, 1) = TY(j, 1) + 1;
                break
            end
        end
    end
    PY = (TY + lambda)/(size(Y, 1) + lambda * size(YValue, 1));
    %計算條件概率
    pX_Y=cell(size(YValue, 1), size(X, 2));
    for k=1:1:size(YValue, 1)
        %條件y＝yk
        for i=1:1:size(X, 2)
            %i為特徵編號
            %取得第i個特徵的取值集合
            XAi = AValues{i, 1};
            TXij_Y = zeros(size(XAi, 1), 1);
            for j=1:1:size(XAi, 1)
                %查詢資料中所有Y＝yk且特徵i的值為Aij的資料個數並累加
                for t=1:1:size(X, 1)
                    if(Y(t, 1)==YValue(k, 1) && X(t, i) == XAi(j, 1))
                        TXij_Y(j, 1) = TXij_Y(j, 1) + 1;
                    end
                end
            end
            PX_Y{k, i} = (TXij_Y + lambda)/(TY(k, 1) + lambda * size(XAi, 1));
        end
    end
    theta = cell(2,1);
    theta{1,1} = PX_Y;
    theta{2,1} = PY;
end