Regression analysis is an important method to study relationships between runoff and sediment yield in small watersheds42. In this study, the statistical analysis software (Excel & SPSS) was used to analyse the runoff and sediment relationships of typical rainstorm events43. Besides, Cluster Analysis (MATLAB Procedure) is an important approach of unsupervised learning44. As a data analysis tool, its importance has been widely recognized in various fields. A Cluster Analysis is performed in order to find the ‘natural grouping’ of data sets, which is also called a ‘cluster’. Generally, a cluster is a collection of similar elements. Similarity coefficient and distance are two important parameters of Cluster Analysis. The similarity coefficient is indicative of the similarity degree between different sample variables, the range is 0–1. When its value is close to 1, the similarity degree between samples is strong. If the value is 0, there is no correlation between samples. Distance represents the geometric distance between different points, and the distance is related to the attributes of the sample points. The basic idea of Cluster Analysis is: first “n” samples are classified as one class separately, and the most similar of them is classified as a new class, at this point, the number of categories becomes “n − 1”. Then, the similarity between the new class and other “n − 2” classes is calculated, and the nearest approximation is classified as another new class, the total class number becomes “n − 2”. By analogy, the process continues until all variables are classified as one category. This clustering process can be expressed by the cluster map. This study used 153 data sets of 17 sets and 9 categories as the sample data (Table 1). Firstly, these data are standardized to eliminate the dimensional differences, so that the indexes are comparable. Secondly, the distance or similarity coefficient between different variables is calculated. Then, the appropriate classification methods are selected and used to progressively cluster samples.Table 1Rainfall runoff and sediment yield parameters and Cluster Analysis results during 17 event-based rainstorms.DateCluster resultsRainfall (mm)Runoff yield time (s)Mean flow (m3/s)Peak flow (m3/s)Total flow (m3)Runoff depth (mm)Runoff coefficientMean sediment concentration (g/cm3)Suspended sediment discharge (t)Sediment yield modulus (t/km2)1997–4–5113.490000.00730.011180.510.00970.00070.48038.654.671997-6-5116.475600.00670.009448.990.00590.00040.37918.562.241997-28-7214.2162000.00960.0151141.370.01710.00120.39255.406.701998-21-5256.4198000.01060.0174310.950.03760.00070.07021.712.631998-23-6524.6162002.603412.24216051.591.94090.09270.1963140.76379.781998-12-7220.9234000.00860.014228.590.02760.00130.10423.732.871998-20-8230.6162000.25670.62082826.80.34180.01120.049139.7016.892000-7-7534.8150002.39867.481117602.542.12850.06120.2604570.58552.672000-14-7641.0176404.504713.277744026.095.32360.12980.24810920.671320.522000-26-7844.5144008.926317.295464942.417.85280.17650.25616618.762009.522000-11-8716.3144002.41285.232936247.424.38300.26970.2047399.33894.722001-26-7546.7126001.30014.727617283.952.09000.04480.1021759.51212.762001-16-8431.8136803.50627.581426541.133.20930.10090.1243296.41398.602008-28-6518.6162001.32112.021516774.842.02840.10910.0831394.09168.572009-7-7134.554000.00690.009419.110.00230.00010.0140.260.032010-11-8355.630004.00906.073112852.171.55410.03330.076970.77117.382010-18-8340.536002.29243.45778032.220.97120.02080.023185.9522.48Note: The similarity coefficient value is 0.8267 by programming calculation of Cluster Analysis.