Dimensionality reduction methods and clustering algorithms for large data set - r

Question

my data set has got 17 columns and > 80.000 variables. The data set consists entirely of numeric variables. Some columns are dummy variables. I want to use my data set to apply different hard and soft clustering algorithms and compare them. Which methods of dimension reduction and clustering algorithms are recommended for large data sets?
Here is a part of my dataset:
dput(rbind(head(WKA_ohneJB, 10), tail(WKA_ohneJB, 10)))
structure(list(X = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
821039L, 821040L, 821041L, 821042L, 821043L, 821044L, 821045L,
821046L, 821047L, 821048L), BASKETS_NZ = c(1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L),
LOGONS = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), PIS = c(71L, 39L, 50L, 4L,
13L, 4L, 30L, 65L, 13L, 31L, 111L, 33L, 3L, 46L, 11L, 8L,
17L, 68L, 65L, 15L), PIS_AP = c(14L, 2L, 4L, 0L, 0L, 0L,
1L, 0L, 2L, 1L, 13L, 0L, 0L, 2L, 1L, 0L, 3L, 8L, 0L, 1L),
PIS_DV = c(3L, 19L, 4L, 1L, 0L, 0L, 6L, 2L, 2L, 3L, 38L,
8L, 0L, 5L, 2L, 0L, 1L, 0L, 3L, 2L), PIS_PL = c(0L, 5L, 8L,
2L, 0L, 0L, 0L, 24L, 0L, 6L, 32L, 8L, 0L, 0L, 4L, 0L, 0L,
0L, 0L, 0L), PIS_SDV = c(18L, 0L, 11L, 0L, 0L, 0L, 0L, 0L,
0L, 1L, 6L, 0L, 0L, 13L, 0L, 0L, 1L, 15L, 1L, 0L), PIS_SHOPS = c(3L,
24L, 13L, 3L, 0L, 0L, 6L, 28L, 2L, 11L, 71L, 16L, 2L, 5L,
6L, 0L, 1L, 0L, 3L, 2L), PIS_SR = c(19L, 0L, 14L, 0L, 0L,
0L, 2L, 23L, 0L, 3L, 6L, 0L, 0L, 20L, 0L, 0L, 3L, 32L, 1L,
0L), QUANTITY = c(13L, 2L, 18L, 1L, 14L, 1L, 4L, 2L, 5L,
1L, 5L, 2L, 2L, 4L, 1L, 3L, 2L, 8L, 17L, 8L), WKA = c(1L,
1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L,
0L, 0L, 1L, 1L), NEW_CUST = c(0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), EXIST_CUST = c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L), WEB_CUST = c(1L, 0L, 0L, 0L, 1L, 1L, 0L,
1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L), MOBILE_CUST = c(0L,
1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
1L, 0L, 1L, 0L), TABLET_CUST = c(0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L),
LOGON_CUST_STEP2 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L)), row.names = c(1L,
2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 821039L, 821040L, 821041L,
821042L, 821043L, 821044L, 821045L, 821046L, 821047L, 821048L
), class = "data.frame")

Answer 1

17x80000 is not so large. You should be able to apply any clustering method on this dataset. It is hard to tell what will work best not knowing the data and the problem in detail. Have a look at "Introduction to Statistical Learning", Ch. 10 for clustering methods. There are also some very instructive R labs for this chapter, which should give you a very quick start.
For further reading also consider "Elements of Statistical Learning" (Chapter 13 onwards).