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Abstract The stochastic approximation method under different distance measures is implemented in clustering of joint orientation data and the performance of different validity indices is investigated by case study. The clustering results indicate that the Euclidean，arc-length and sine-squared distance measures are all proved to be suitable for clustering analysis. But the performance of validity indices is found to be different under different distance measures. The index CH works only under arc-length distance measure. The index I is effective under Euclidean and sine-squared distance measures，while the indices DB and XB are found to be applicable under all three measures. The difference between validity index and objective function in determining the best clustering results is also studied. Only under sine-squared distance measure，the index I and the objective function give the same clustering results. Thereby the combination of sine-squared distance and I index is proposed to be the best solution to clustering of orientation data. The in situ data of Beishan deep rock mass are then successfully classified with the above combination scheme.
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2015, Vol. 34 
