Question

我试图使用以下代码绘制k的肘部：

load CSDmat %mydata
for k = 2:20
    opts = statset('MaxIter', 500, 'Display', 'off');
    [IDX1,C1,sumd1,D1] = kmeans(CSDmat,k,'Replicates',5,'options',opts,'distance','correlation');% kmeans matlab
    [yy,ii] = min(D1');      %% assign points to nearest center

    distort = 0;
    distort_across = 0;
    clear clusts;
    for nn=1:k
        I = find(ii==nn);       %% indices of points in cluster nn
        J = find(ii~=nn);       %% indices of points not in cluster nn
        clusts{nn} = I;         %% save into clusts cell array
        if (length(I)>0)
            mu(nn,:) = mean(CSDmat(I,:));               %% update mean
            %% Compute within class distortion
            muB = repmat(mu(nn,:),length(I),1);
            distort = distort+sum(sum((CSDmat(I,:)-muB).^2));
            %% Compute across class distortion
            muB = repmat(mu(nn,:),length(J),1);
            distort_across = distort_across + sum(sum((CSDmat(J,:)-muB).^2));
        end
    end
    %% Set distortion as the ratio between the within
    %% class scatter and the across class scatter
    distort = distort/(distort_across+eps);

        bestD(k)=distort;
        bestC=clusts;
end
figure; plot(bestD);

bestD的值（在群集方差/群集方差之间）是

[
0.401970132754914
0.193697163350293
0.119427184084282
0.0872681777446508
0.0687948264457301
0.0566215549396577
0.0481117619129058
0.0420491551659459
0.0361696583755145
0.0320384092689509
0.0288948343304147
0.0262373245283877
0.0239462330460614
0.0218350896369853
0.0201506779033703
0.0186757121130685
0.0176258625858971
0.0163239661159014
0.0154933431470081
]

该代码改编自2005年3月加州理工学院的Lihi Zelnik-Manor。

群集方差与群集方差之间的地积比率是一条平滑的曲线，其膝盖像曲线一样平滑，上面给出的曲线bestD数据。我们如何为这些图找到膝盖？

Answer 1

我认为最好只使用“类内失真”作为优化参数：

%% Compute within class distortion
muB = repmat(mu(nn,:),length(I),1);
distort = distort+sum(sum((CSDmat(I,:)-muB).^2));

使用此不用将此值除以“distort_across”。如果你计算这个的“衍生物”：

unexplained_error = within_class_distortion;
derivative = diff(unexplained_error);
plot(derivative)

导数（k）通过添加新群集告诉您未解释的错误减少了多少。我建议您在此错误的减少量小于您获得的第一次减少量的十倍时停止添加群集。

for (i=1:length(derivative))
    if (derivative(i) < derivative(1)/10)
         break
    end
end
k_opt = i+1;

实际上，获得最佳簇数的方法取决于应用，但我认为您可以使用此建议获得k的良好值。

K表示当肘部曲线是平滑曲线时找到肘部

1 个答案: