聚类中的大距离矩阵

Question

我在具有 16 GB RAM 的机器上运行 R 3.2.3。我有一个 3,00,000 行 x 12 列的大矩阵。我想在 R 中使用层次聚类算法，所以在我这样做之前，我正在尝试创建一个距离矩阵。由于数据是混合类型的，我对不同的类型使用不同的矩阵。我收到有关内存分配的错误：

df <- as.data.frame(matrix(rnorm(36*10^5), nrow = 3*10^5))
d1=as.dist(distm(df[,c(1:2)])/10^5)
d2=dist(df[,c(3:8)], method = "euclidean") 
d3= hamming.distance(df[,c(9:12)]%>%as.matrix(.))%>%as.dist(.)

我收到以下错误

> d1=as.dist(distm(df1[,c(1:2)])/10^5)
Error: cannot allocate vector of size 670.6 Gb
In addition: Warning messages:
1: In matrix(0, ncol = n, nrow = n) :
Reached total allocation of 16070Mb: see help(memory.size)
2: In matrix(0, ncol = n, nrow = n) :
Reached total allocation of 16070Mb: see help(memory.size)
3: In matrix(0, ncol = n, nrow = n) :
Reached total allocation of 16070Mb: see help(memory.size)
4: In matrix(0, ncol = n, nrow = n) :
Reached total allocation of 16070Mb: see help(memory.size)
> d2=dist(df1[,c(3:8)], method = "euclidean") 
Error: cannot allocate vector of size 335.3 Gb
In addition: Warning messages:
1: In dist(df1[, c(3:8)], method = "euclidean") :
 Reached total allocation of 16070Mb: see help(memory.size)
2: In dist(df1[, c(3:8)], method = "euclidean") :
Reached total allocation of 16070Mb: see help(memory.size)
3: In dist(df1[, c(3:8)], method = "euclidean") :
Reached total allocation of 16070Mb: see help(memory.size)
4: In dist(df1[, c(3:8)], method = "euclidean") :
Reached total allocation of 16070Mb: see help(memory.size)
> d3= hamming.distance(df1[,c(9:12)]%>%as.matrix(.))%>%as.dist(.)
Error: cannot allocate vector of size 670.6 Gb
In addition: Warning messages:
1: In matrix(0, nrow = nrow(x), ncol = nrow(x)) :
Reached total allocation of 16070Mb: see help(memory.size)
2: In matrix(0, nrow = nrow(x), ncol = nrow(x)) :
Reached total allocation of 16070Mb: see help(memory.size)
3: In matrix(0, nrow = nrow(x), ncol = nrow(x)) :
Reached total allocation of 16070Mb: see help(memory.size)
4: In matrix(0, nrow = nrow(x), ncol = nrow(x)) :
Reached total allocation of 16070Mb: see help(memory.size)

Answer 1

为简单起见，假设您有 1 行 (A) 以最小距离与 3^8 矩阵 (B) 进行聚类。

原来的做法是：

1. load A and B
2. distance compute A with each row of B
3. select smallest one from results (reduction)

但是因为B真的很大，所以不能加载到内存或者执行过程中报错。

批处理方法将如下所示：

1. load A (suppose it is small)
2. load B.partial with 1 to 1^5 rows of B
3. compute distance of A with each row of B.partial
4. select min one in partial results and save it as res[i]
5. go back 2.) load next 1^5 rows of B 
6. final your got a 3000 partial results and saved in res[1:3000]
7. reduction : select min one from res[1:3000]
   note: if you need all distances as `dist` function, you don't need reduction and just keep this array.

代码会比原来的要复杂一些。但是当我们处理大数据问题时，这是非常常见的技巧。对于计算部分，您可以参考我之前在here 中的答案之一。

如果您可以在此处粘贴带有批处理模式的最终代码，我将非常合适。以便其他人也可以学习。

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另一个有趣的事情 dist 是R 包中支持openMP 的少数几个。查看here 中的源代码以及here 中如何使用openMP 进行编译。

所以，如果您可以尝试根据您的机器将OMP_NUM_THREADS 设置为 4 或 8，然后再次运行，您可以看到性能提升很多！

 void R_distance(double *x, int *nr, int *nc, double *d, int *diag,
    int *method, double *p)
{
     int dc, i, j;
     size_t  ij;  /* can exceed 2^31 - 1 */
     double (*distfun)(double*, int, int, int, int) = NULL;
     #ifdef _OPENMP
        int nthreads;
     #endif
     .....
 }

另外，如果你想通过GPU加速dist，可以参考ParallelR中的talk部分。