使用kernlab包kkmeans函数时聚类数相关报错问题

我用R的kernlab包中kkmeans()函数做核K均值聚类，部分聚类数能正常返回结果，但指定其他聚类数时会抛出错误：

Error in if (sum(abs(dc)) < 1e-15) break : missing value where TRUE/FALSE needed

观察到报错常出现在聚类数增加时，但样本量远大于聚类数：比如8000行×3列的矩阵指定10类正常，指定100类报错；50行子集指定5类正常，指定10类报错。

以下是可复现的最小示例：

指定centers = 10时报错 #

kernlab::kkmeans(mymat, centers=10)
#> Using automatic sigma estimation (sigest) for RBF or laplace kernel
#> Error in if (sum(abs(dc)) < 1e-15) break: missing value where TRUE/FALSE needed

指定centers = 5时无报错 #

kernlab::kkmeans(mymat, centers=5)
#> Using automatic sigma estimation (sigest) for RBF or laplace kernel
#> Spectral Clustering object of class "specc" 
#> 
#>  Cluster memberships: 
#>  
#> 1 1 1 1 2 1 1 3 3 5 5 5 3 2 2 2 4 4 3 3 5 2 2 5 5 5 5 5 5 2 4 3 3 3 2 2 5 3 3 5 5 4 4 4 3 1 4 2 5 3 
#>  
#> Gaussian Radial Basis kernel function. 
#>  Hyperparameter : sigma =  0.756590498067127 
#> 
#> Centers:  
#>          [,1]      [,2]     [,3]
#> [1,] 15.75871 -16.69486 191.5841
#> [2,] 16.74850 -21.94730 186.8914
#> [3,] 15.99483 -18.95892 190.2622
#> [4,] 15.45729 -18.13571 191.9611
#> [5,] 16.69136 -22.19600 187.0055
#> 
#> Cluster size:  
#> [1]  7 10 12  7 14
#> 
#> Within-cluster sum of squares:  
#> [1] 301006.7 443237.8 607889.4 305777.1 685823.5

示例数据（50×3矩阵） #

mymat <- structure(c(15.9390001296997, 15.9079999923706, 16.087999343872, 
15.7930002212524, 15.9619998931884, 15.6129999160766, 15.7550001144409, 
16.7740001678466, 16.9080009460449, 17.0769996643066, 16.3640003204345, 
16.5960006713867, 16.579999923706, 16.4570007324218, 16.2320003509521, 
16.1639995574951, 15.6180000305175, 15.5109996795654, 15.5120000839233, 
15.628999710083, 16.9950008392333, 17.3530006408691, 17.2229995727539, 
16.8910007476806, 17.1800003051757, 17.1709995269775, 16.9860000610351, 
16.704999923706, 16.273000717163, 15.8830003738403, 15.6230001449584, 
15.333999633789, 15.3839998245239, 15.3870000839233, 17.1119995117187, 
17.6200008392333, 16.8349990844726, 16.4969997406005, 16.2479991912841, 
16.1259994506835, 15.8059997558593, 15.378999710083, 15.4320001602172, 
15.2100000381469, 15.2519998550415, 15.2150001525878, 15.4280004501342, 
17.4790000915527, 16.6739997863769, 16.4330005645751, -16.6299991607666, 
-16.9529991149902, -17.5610008239746, -17.8290004730224, -18.6200008392333, 
-17.1079998016357, -16.25, -21.716999053955, -21.1219997406005, 
-21.8209991455078, -20.1840000152587, -20.0450000762939, -20.9599990844726, 
-19.5240001678466, -18.6590003967285, -19.4379997253417, -18.6280002593994, 
-18.0669994354248, -16.204999923706, -15.5830001831054, -23.9489994049072, 
-23.57200050354, -24.3969993591308, -23.2880001068115, -22.6019992828369, 
-23.2329998016357, -22.5979995727539, -22.6140003204345, -20.8059997558593, 
-19.4300003051757, -19.4729995727539, -17.5690002441406, -16.8110008239746, 
-15.2930002212524, -25.2509994506835, -24.7649993896484, -24.8080005645751, 
-21.9939994812011, -21.5189990997314, -20.329999923706, -20.25, 
-19.1380004882812, -18.6180000305175, -18.5900001525878, -16.1620006561279, 
-14.5329999923706, -14.4359998703002, -25.8169994354248, -24.2159996032714, 
-22.57200050354, 190.996994018554, 190.996002197265, 190.18699645996, 
191.039993286132, 190.205993652343, 191.919006347656, 191.766006469726, 
187.14599609375, 186.889007568359, 186.225997924804, 188.60400390625, 
187.932006835937, 187.837005615234, 188.453002929687, 189.382995605468, 
189.360000610351, 191.25, 191.845001220703, 192.580001831054, 
192.414993286132, 185.358001708984, 184.570999145507, 184.595993041992, 
186.091995239257, 185.613998413085, 185.25, 186.235000610351, 
187.003005981445, 188.744995117187, 190.169998168945, 190.921005249023, 
192.628997802734, 192.768005371093, 193.281997680664, 184.602996826171, 
183.796005249023, 185.414001464843, 187.811004638671, 188.615005493164, 
189.263000488281, 190.167007446289, 191.781997680664, 191.837997436523, 
192.582000732421, 193.399002075195, 194.184005737304, 193.509994506835, 
183.776000976562, 186.173995971679, 187.774993896484), dim = c(50L, 
3L), dimnames = list(NULL, c("x", "y", "z")))

这个报错本质是算法迭代过程中出现了空聚类，导致计算出现NA值，进而让判断条件无法执行（NA不能参与TRUE/FALSE判断）。针对这个问题，有几个可行的解决思路：

1. 手动指定核函数的sigma参数 #

默认的sigest自动估计sigma在聚类数较多时，可能生成不合适的核宽度，导致样本过度分散出现空聚类。可以手动尝试不同的sigma值：

# 用样本标准差的倍数手动设置sigma
sigma_val <- sd(as.vector(mymat)) * 0.5
# 指定sigma运行kkmeans
kernlab::kkmeans(mymat, centers=10, kernel="rbfdot", kpar=list(sigma=sigma_val))

2. 调整迭代参数 #

通过增加最大迭代次数、放宽收敛阈值，给算法更多收敛空间：

kernlab::kkmeans(mymat, centers=10, iter.max=1000, epsilon=1e-10)

3. 选择合理的聚类数 #

当聚类数接近样本天然簇数量时，强行划分更多聚类会导致空簇。可以先用肘部法则、轮廓系数等方法评估最优聚类数，再指定centers值。

4. 标准化数据 #

对数据做z-score标准化，让特征尺度一致，有助于核函数稳定计算相似度：

mymat_scaled <- scale(mymat)
kernlab::kkmeans(mymat_scaled, centers=10)

内容的提问来源于stack exchange，提问作者myfatson