How to find similar density curves?

Question

I've dataset with player game by game performance rating and my goal is to group them based on density curves. Below there is plot with density curves of five random players. We can see that red and purple density curves are similar, but is there any metric or function in R which would help me to group those curves when there're let's say 50 of them on the plot? I want to group them on at least 3-4 groups, for example first group would be mentioned red and purple lines which represents players with more good games than bad games.

Plot

Simple code for plot and sample data: Columns: TOTAL.QBR - player game rating ID - unique for every player

library(sm)

newdata <- structure(list(TOTAL.QBR = c(16.9, 21.1, 22.1, 34.8, 53.6, 58.3, 
                                    82, 13, 13.6, 16.3, 18.2, 23.9, 27.3, 27.6, 28.4, 28.6, 29.1, 
                                    32.3, 33.1, 34.8, 36.4, 37.1, 37.2, 37.7, 37.8, 39.3, 40.4, 41.8, 
                                    42.4, 44.3, 44.5, 47, 47.3, 48.1, 48.7, 49, 49.3, 49.4, 49.8, 
                                    50.2, 51, 51.5, 53.5, 53.5, 53.5, 53.6, 55.4, 55.5, 56, 56.3, 
                                    56.5, 57, 57.3, 59.6, 60.5, 62.2, 62.8, 62.8, 63.3, 64.5, 65.4, 
                                    65.5, 66.4, 67.2, 67.3, 67.4, 67.6, 68.9, 68.9, 69.1, 69.3, 69.9, 
                                    71.5, 71.9, 72.5, 72.9, 73.4, 74.1, 74.4, 74.9, 75.2, 75.2, 75.8, 
                                    75.9, 76.6, 77.1, 78.2, 78.2, 78.4, 78.6, 78.7, 79.3, 79.8, 79.9, 
                                    81.6, 81.8, 82.4, 82.4, 82.9, 82.9, 83.2, 83.5, 83.6, 83.7, 84, 
                                    84.4, 84.7, 84.8, 84.9, 85.7, 87.4, 87.8, 88.1, 88.4, 88.5, 88.8, 
                                    89.1, 89.4, 89.4, 89.4, 89.5, 90.9, 92.2, 92.7, 93, 93.5, 93.6, 
                                    94.9, 95.1, 95.4, 95.6, 96.6, 96.7, 97.6, 97.8, 98.4, 98.6, 99.4, 
                                    26.2, 34.6, 42.7, 87, 1.4, 5, 6.8, 7.7, 8.3, 9.6, 9.9, 10.1, 
                                    11.1, 12.5, 12.7, 12.9, 13.1, 13.9, 14.3, 14.6, 15.8, 16.6, 19.3, 
                                    20.8, 22.8, 23, 23.5, 26.4, 27.2, 28, 30.3, 30.8, 30.9, 31.4, 
                                    31.5, 31.8, 32.1, 32.5, 32.6, 33.3, 33.3, 33.9, 34.6, 34.7, 34.7, 
                                    34.8, 35.8, 36.8, 37.2, 37.9, 39.9, 40.4, 40.8, 41.1, 41.8, 43.7, 
                                    44.2, 45, 45.9, 46.9, 47.2, 47.3, 47.6, 47.8, 49.1, 49.1, 49.3, 
                                    51.7, 53.3, 53.6, 54.2, 56.2, 56.4, 56.4, 56.6, 56.9, 59.2, 59.6, 
                                    59.7, 59.8, 60, 60.6, 60.8, 61.6, 62, 62.8, 62.9, 62.9, 63.7, 
                                    64.5, 65, 65, 65.9, 67.5, 67.6, 67.6, 68.4, 68.8, 69.3, 70.4, 
                                    71.2, 71.9, 74, 74.3, 75.4, 76.6, 77.4, 77.5, 77.7, 78, 79.2, 
                                    79.2, 79.4, 80.1, 80.7, 81.7, 81.8, 82.7, 83.6, 85, 85.5, 86.7, 
                                    87.5, 88.5, 90.1, 90.3, 90.6, 90.7, 92.4, 92.4, 93.1, 93.5, 95.3, 
                                    95.7, 95.9, 98.2, 8.5, 9.1, 13.7, 17.6, 23.3, 26.1, 26.4, 27.1, 
                                    29.7, 30.4, 33, 36.1, 37.9, 41.5, 42.7, 45, 45.5, 45.5, 46, 46.9, 
                                    49.9, 50.6, 50.7, 53.4, 53.5, 56.3, 57.4, 57.9, 58.6, 58.7, 60.2, 
                                    60.7, 61.8, 62.2, 62.9, 64.4, 65.6, 66.7, 67, 67.4, 68.2, 68.2, 
                                    68.8, 72, 72.9, 73.2, 74.5, 75.8, 76.4, 76.6, 77.6, 79.9, 80.4, 
                                    81.2, 81.4, 81.8, 82.8, 84.6, 85.1, 87.2, 87.9, 90, 91.7, 94.5, 
                                    94.8, 95.5, 98.4, 1.4, 1.6, 5.6, 9.4, 17.6, 19.5, 24.5, 34.9, 
                                    39.6, 42.4, 59, 1, 2.6, 3.1, 5.5, 7.1, 14.8, 15.9, 19.5, 20.1, 
                                    21.8, 21.9, 22, 22.8, 25.7, 26.5, 26.5, 26.6, 27.2, 27.8, 28.6, 
                                    31, 31.6, 32.4, 34.1, 36, 36.5, 37.6, 38.2, 38.2, 39, 39.1, 39.2, 
                                    39.7, 40.3, 40.3, 40.6, 40.6, 41.2, 44.4, 46.2, 47, 47.1, 47.2, 
                                    47.4, 47.7, 48, 48.3, 48.5, 48.7, 49.9, 50.4, 50.7, 51.2, 52, 
                                    52.2, 52.2, 52.6, 53.7, 55.7, 55.8, 57.6, 58.8, 61.3, 62.4, 62.4, 
                                    63.4, 63.6, 63.7, 63.9, 64.6, 66.3, 67.1, 68.5, 69.4, 69.6, 69.9, 
                                    70.5, 71.8, 75.8, 76.4, 77.2, 77.4, 78.8, 79.2, 80.5, 81.7, 82.1, 
                                    82.4, 83.2, 83.7, 85.4, 89, 90.5, 90.5, 91.1, 92.2, 92.4, 94.9, 
                                    96.9, 98.1, 4.1, 8.3, 10.3, 11.4, 12.2, 12.2, 12.9, 14.4, 18.5, 
                                    18.7, 18.7, 19.8, 20.9, 21.8, 22.7, 25.9, 25.9, 26, 28.3, 28.3, 
                                    28.5, 28.8, 30.9, 32.3, 33.7, 34, 34.5, 36.6, 36.7, 37.8, 38.3, 
                                    38.5, 39.9, 41.4, 43.4, 43.6, 44, 44.2, 45.1, 45.4, 45.5, 45.6, 
                                    46.3, 46.3, 47.1, 47.5, 48.8, 49.7, 49.9, 51.4, 52.2, 53.1, 54.5, 
                                    54.8, 55.8, 56, 56.2, 57.7, 58.2, 58.3, 58.3, 58.8, 58.9, 60.5, 
                                    60.6, 60.8, 61.4, 61.4, 61.6, 61.7, 63.6, 64.4, 64.5, 64.7, 64.8, 
                                    65, 65.4, 65.6, 65.6, 65.8, 66.2, 66.5, 69.6, 69.7, 69.8, 70.1, 
                                    70.4, 71, 71.3, 71.7, 71.7, 71.9, 72.5, 73.4, 73.4, 74.4, 74.7, 
                                    74.9, 75.2, 75.5, 76, 76.3, 76.5, 76.6, 76.8, 77.2, 78.1, 78.3, 
                                    78.7, 79, 79.7, 79.9, 81, 81.2, 81.3, 81.6, 82.6, 82.7, 82.9, 
                                    83, 83.5, 83.5, 83.6, 83.8, 83.8, 84, 84.4, 84.5, 85.3, 85.3, 
                                    85.3, 85.5, 86.2, 86.2, 86.6, 86.6, 86.7, 87, 87.1, 87.2, 87.4, 
                                    87.9, 88.3, 88.4, 88.5, 89, 89.4, 90.4, 90.5, 91.1, 91.4, 92.3, 
                                    93.8, 94.7, 95.2, 95.6, 95.9, 96, 96.2, 96.3, 97.4, 98.9, 99.1, 
                                    99.2), ID = c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
                                                  3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 
                                                  4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                  5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
                                                  6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
                                                  6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
                                                  6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
                                                  6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
                                                  7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                  8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
                                                  10L, 10L)), row.names = c(5197L, 5571L, 5513L, 5633L, 5533L, 
                                                                            5476L, 5432L, 4493L, 2658L, 3748L, 1245L, 1357L, 1960L, 1800L, 
                                                                            631L, 3470L, 3778L, 4291L, 1064L, 2019L, 4458L, 3391L, 892L, 
                                                                            710L, 1374L, 1163L, 4697L, 1591L, 2537L, 1403L, 3986L, 3419L, 
                                                                            2617L, 4103L, 2705L, 4601L, 1473L, 3808L, 2399L, 48L, 3959L, 
                                                                            3437L, 1176L, 2426L, 4350L, 1982L, 2327L, 2867L, 734L, 4665L, 
                                                                            2366L, 528L, 2453L, 405L, 80L, 647L, 1914L, 4626L, 3050L, 4163L, 
                                                                            587L, 1083L, 3103L, 939L, 1281L, 3882L, 2038L, 1313L, 4009L, 
                                                                            3204L, 9L, 839L, 4538L, 1255L, 1882L, 1430L, 2920L, 4504L, 1817L, 
                                                                            2795L, 2759L, 2884L, 4067L, 4245L, 3167L, 2667L, 104L, 1127L, 
                                                                            1689L, 1488L, 999L, 3601L, 750L, 5022L, 1720L, 1195L, 3286L, 
                                                                            3925L, 810L, 3077L, 486L, 3315L, 1519L, 2965L, 4128L, 4031L, 
                                                                            967L, 1750L, 2549L, 3568L, 4559L, 3015L, 1023L, 3347L, 4365L, 
                                                                            665L, 2818L, 1547L, 4214L, 4304L, 3130L, 2725L, 3535L, 2936L, 
                                                                            777L, 3692L, 1655L, 3899L, 899L, 2469L, 4391L, 1840L, 3480L, 
                                                                            546L, 2059L, 3221L, 4183L, 1628L, 1380L, 1327L, 1295L, 1335L, 
                                                                            5370L, 2315L, 1742L, 4987L, 2495L, 3995L, 1415L, 1015L, 3689L, 
                                                                            544L, 4931L, 4958L, 2959L, 91L, 1044L, 2517L, 5546L, 4146L, 1991L, 
                                                                            2022L, 3968L, 3182L, 4112L, 1067L, 2876L, 4792L, 3304L, 5389L, 
                                                                            5510L, 3448L, 5309L, 313L, 4023L, 1957L, 1832L, 893L, 3120L, 
                                                                            2153L, 1698L, 4725L, 4818L, 5601L, 3367L, 741L, 2073L, 144L, 
                                                                            3329L, 283L, 378L, 2901L, 3932L, 1762L, 201L, 1324L, 5415L, 5188L, 
                                                                            2098L, 228L, 5444L, 4167L, 847L, 5628L, 1893L, 3417L, 501L, 1175L, 
                                                                            5251L, 1557L, 3052L, 5215L, 1086L, 1585L, 791L, 3028L, 1367L, 
                                                                            44L, 974L, 3639L, 1637L, 1262L, 555L, 1282L, 2206L, 3234L, 3085L, 
                                                                            1784L, 1912L, 2392L, 2172L, 673L, 423L, 455L, 3729L, 1466L, 4070L, 
                                                                            641L, 3135L, 3379L, 2035L, 1428L, 1663L, 3201L, 1098L, 1607L, 
                                                                            1196L, 395L, 2231L, 2356L, 2422L, 935L, 1485L, 4033L, 904L, 5554L, 
                                                                            156L, 2819L, 609L, 2990L, 2260L, 1332L, 2L, 1220L, 809L, 2910L, 
                                                                            747L, 2523L, 98L, 5263L, 324L, 3897L, 1120L, 2443L, 1838L, 1117L, 
                                                                            2130L, 689L, 1706L, 1040L, 2183L, 2220L, 1013L, 2489L, 1862L, 
                                                                            1563L, 2680L, 2100L, 2708L, 2737L, 848L, 1789L, 1134L, 1402L, 
                                                                            1588L, 561L, 1761L, 944L, 978L, 915L, 2766L, 2365L, 589L, 2007L, 
                                                                            2610L, 2269L, 2452L, 1915L, 2530L, 2326L, 1492L, 698L, 525L, 
                                                                            2236L, 618L, 2503L, 2294L, 2639L, 489L, 1429L, 1079L, 2139L, 
                                                                            1608L, 2384L, 2034L, 1722L, 1658L, 749L, 2420L, 2792L, 2581L, 
                                                                            2550L, 1942L, 1517L, 637L, 1971L, 869L, 1145L, 1452L, 1874L, 
                                                                            806L, 4495L, 5369L, 4617L, 5395L, 5228L, 5573L, 5287L, 5600L, 
                                                                            5418L, 5303L, 5328L, 31L, 2163L, 1653L, 416L, 2749L, 1804L, 2909L, 
                                                                            181L, 772L, 1565L, 60L, 2514L, 1836L, 2715L, 802L, 3152L, 381L, 
                                                                            1478L, 742L, 2491L, 2775L, 2461L, 3058L, 2375L, 256L, 2101L, 
                                                                            1136L, 1732L, 2123L, 596L, 682L, 1406L, 1926L, 438L, 470L, 1185L, 
                                                                            2215L, 1985L, 1955L, 1500L, 1857L, 2834L, 887L, 3113L, 310L, 
                                                                            2275L, 946L, 3174L, 84L, 535L, 503L, 3089L, 3267L, 2331L, 1440L, 
                                                                            1613L, 917L, 193L, 222L, 2866L, 2998L, 2611L, 1581L, 840L, 2673L, 
                                                                            554L, 1154L, 3233L, 2557L, 1003L, 1197L, 1692L, 106L, 2640L, 
                                                                            334L, 1053L, 2945L, 2387L, 2000L, 1753L, 2291L, 3020L, 1880L, 
                                                                            2916L, 2230L, 1253L, 639L, 266L, 968L, 1518L, 2577L, 2414L, 606L, 
                                                                            2030L, 1022L, 1218L, 1073L, 1654L, 807L, 2058L, 635L, 4442L, 
                                                                            5015L, 2782L, 4299L, 5261L, 715L, 862L, 5488L, 4464L, 4614L, 
                                                                            2077L, 4114L, 5227L, 1900L, 1356L, 1536L, 1445L, 4174L, 5512L, 
                                                                            1140L, 1649L, 2250L, 87L, 2844L, 5361L, 113L, 2339L, 3211L, 1733L, 
                                                                            3906L, 1860L, 3987L, 1161L, 2119L, 3442L, 141L, 764L, 2455L, 
                                                                            5597L, 1954L, 3860L, 2952L, 4513L, 3466L, 5095L, 5066L, 2704L, 
                                                                            5274L, 3522L, 3612L, 2561L, 3957L, 3580L, 558L, 306L, 4348L, 
                                                                            3264L, 5380L, 1495L, 4568L, 2093L, 4540L, 4484L, 1916L, 2997L, 
                                                                            1230L, 1399L, 3636L, 527L, 1467L, 336L, 2732L, 2296L, 5438L, 
                                                                            246L, 4661L, 3104L, 4247L, 3675L, 186L, 3137L, 813L, 3701L, 2140L, 
                                                                            877L, 2169L, 726L, 2886L, 1665L, 2587L, 7L, 3487L, 2001L, 2036L, 
                                                                            1026L, 4745L, 908L, 3022L, 4622L, 5023L, 271L, 3759L, 2357L, 
                                                                            4395L, 1308L, 2475L, 2499L, 2793L, 583L, 4064L, 1813L, 361L, 
                                                                            4004L, 3877L, 3046L, 157L, 3165L, 4833L, 487L, 419L, 451L, 5401L, 
                                                                            2419L, 3406L, 4966L, 4127L, 1361L, 34L, 966L, 1548L, 3789L, 1603L, 
                                                                            1777L, 4710L, 4803L, 5526L, 5612L, 1278L, 1747L, 2850L, 391L, 
                                                                            2911L, 4770L, 4884L, 4185L, 5550L, 3820L, 1168L, 2964L, 2195L, 
                                                                            5315L, 4912L, 3534L, 2520L, 775L, 2257L, 2381L, 1247L, 993L, 
                                                                            5291L, 3722L, 4934L, 1572L), class = "data.frame")


sm.density.compare(newdata$TOTAL.QBR, newdata$ID, ylim=c(0,0.030))

This is too broad. There are all sorts of metrics defined between curves (e.g. the L_2 norm, which is the square root of the integral of the square of the difference between the functions) and all sorts of clustering algorithms which could be applied. It would help if you gave a [mcve] which allows others to experiment with your problem. See [How to make a great R reproducible example?](https://stackoverflow.com/q/5963269/4996248) for what this would mean in R. — John Coleman, Sep 26 '18 at 15:33
And really this is more of a methods question rather than a specific programming question. It's probably a better fit for [stats.se] or [datascience.se]. This really isn't about R; how would you do this with any language? — MrFlick, Sep 26 '18 at 15:42

G. Grothendieck · Accepted Answer · 2018-09-27T12:46:20.733

If there are n curves then represent each curve curve by its values at k points and form the n x k matrix X. Then run

set.seed(123)
kmeans(X, g, nstart = 25)

where the input g is the number of groups you want. This will perform the clustering 25 times using 25 different random starting points and then it will return the best of them.

ADDED

Since posting the above the question added data and some code so using that:

result <- sm.density.compare(newdata$TOTAL.QBR, newdata$ID, ylim=c(0, 0.030),
  model = "equal")
X <- result$est

set.seed(123)
km <- kmeans(X, 3, nstart = 25)

# plot each group in a separate color
ts.plot(t(X), col = km$cl)

An automatic way to find g would be to use the NbClust package. It will estimate g from a number of viewpoints and we could take the value that occurs most often.

library(NbClust)

res <- NbClust(t(X), distance = "euclidean", min.nc = 2, max.nc = 8,
  method = "kmeans")
tab <- table(res$Best.nc[1, ])
g <- as.numeric(names(tab[which.max(tab)]))
g
## [1] 3

score 1 · Answer 2 · answered Sep 26 '18 at 16:22

In general this problem can be cast in terms of a time-series clustering problem. With all the clustering and preprocessing approaches there are.

Since you're not asking for a specific algorithm (metric), but rather a functionality in R here follows a survey for a lot of those packages related and able to deal with your problem in R - just make sure that you understood exactly what your goal is and which clustering algorithm makes sense in your application:

The flexclust package (Leisch 2006) implements many partitional procedures, while the cluster package (Maechler et al. 2017) focuses more on hierarchical procedures and their evaluation; neither of them, however, is specifically targeted at time-series data. Packages like TSdist (Mori et al. 2016) and TSclust (Montero and Vilar 2014) focus solely on dissimilarity measures for time-series, the latter of which includes a single algorithm for clustering based on p values. Another example is the pdc package (Brandmaier 2015), which implements a specific clustering algorithm, namely one based on permutation distributions. The dtw package (Giorgino 2009) implements extensive functionality with respect to DTW, but does not include the lower bound techniques that can be very useful in time-series clustering. Hence, the dtwclust package is probably the way to go and able to provide a consistent and user-friendly way of interacting with classic and new clustering algorithms, taking into consideration the nuances of time-series data.

How to find similar density curves?

2 Answers2

ADDED