Fig 1.
Left figure is u(S) and right figure is v(S).
Fig 2.
A number of the iterations with current clusters for the Old Faithful data set.
The final number of clusters is four.
Fig 3.
A comparison of the clustering in Fig 2 with the K-means output for four clusters.
Fig 4.
A number of the iterations with current clusters for the Galaxy data set.
The final number of clusters is three.
Fig 5.
A number of the iterations with current clusters for the simulated data set.
The final number of clusters is five—the correct number.
Fig 6.
Data set on unit sphere.
Fig 7.
Locations of the eight landmarks.
Fig 8.
Left plot: the coordinates of the first two principal components in the tangent space; Right plot: Landmarks represented by symbols and colours based on the clusterings.
Fig 9.
Data set with 5 clusters and σ2 = 0.2.
Table 1.
The average number of clusters by after adding noise to the five centres with various σ.
Fig 10.
US arrests clusterings from the hierarchical k-means algorithm and the gap method.
Fig 11.
US arrests clustering from the Hungarian algorithm; there are 7 clusters.
Fig 12.
Supporting evidence of 7 clusters for the US arrests data based on view with 3 principal components.