We thoroughly evaluate DCA - GMM on synthetic data generated with different variance level and noise level . The higher of these two levels , the harder the clustering task is . The results are reported in Figure 3 , the detailed procedure generating data and evaluation metrics are given in the caption . On all metrics , DCA - GMM shows a phase transition property , i.e. , the algorithm will overwhelmingly success below a curve of noise and variance level . This property verifies the robustness of DCA - GMM to data noise and variance within a cluster . In addition , when increasing the number of sub - problems ( layers from bottom to top ) , the accuracy of DCA - GMM soon saturates on a value close to 1 , this indicates that a small number of sub - problems in DCA - GMM is sufficient to produce a promising clustering result , which is highly preferred in practice . Moreover , the time cost of DCA - GMM is significantly small and thus exhibits its competitive efficiency . Furthermore , error is more robust to data noise than accuracy , because most false anchors detected in the noise case are close to the true ones , which leads to small error .   Figure 3 : DCA - GMM on synthetic data . On a 30 × 30 grid of different noise level and variance level , for each noise and variance pair , we randomly generate data of k = 5 clusters with 300 , 500 , 400 , 300 , 500 samples respectively , and 3 - view features of 200 , 120 , 160 dimensions respectively . Mean vector of each cluster is added into the data as " anchor " we expect DCA to find out . In particular , each view of points in each cluster are drawn from a multivariate Gaussian distribution with the variance level , and then Gaussian noises of magnitude equal to the noise level are added to the points . We run DCA - GMM using different number of sub - problems , and report their performance by anchor accuracy , clustering accuracy , anchor error ( 2 relative recovery error ) , mutual information and rand index . The CPU seconds are reported too . Each point on each 3D plot is a result of averaging 10 random trials in the same setting , and its height is the value of metric . Each 3D plot includes layers of surfaces associated with different number of sub - problems , we also report the top layer as a 2D plot below each 3D plot .   Figure 4 : Clustering accuracy ( higher is better ) and CPU seconds vs. Number of clusters for Gaussian mixture model on CMU - PIE , YALE , and UMIST human face datasets , UPSP handwritten digit dataset , CIFAR-10 image dataset , and COIL-20 object image dataset . We randomly split the raw pixel features into three groups , each associates to a view in our multi - view model . Baselines : K - means [ 29 ] , EM algorithm , spectral method .