在data.table上按周期分组重复

我有一个包含名称、日期和几个分类列的数据集。让我们说

data <- data.table(name = c('Anne', 'Ben', 'Cal', 'Anne', 'Ben', 'Cal', 'Anne', 'Ben', 'Ben', 'Ben', 'Cal'),
               period = c(1,1,1,1,1,1,2,2,2,3,3), 
               category = c("A","A","A","B","B","B","A","B","A","B","A"))

看起来像这样：

  name  period  category
  Anne       1         A
   Ben       1         A
   Cal       1         A
  Anne       1         B
   Ben       1         B
   Cal       1         B
  Anne       2         A
   Ben       2         B
   Ben       2         A
   Ben       3         A
   Cal       3         B

我想计算，对于每个时期，对于我的每组分类变量，过去时期存在多少个名字。输出应如下所示：

period  category  recurrence_count
    2         A                 2   # due to Anne and Ben being on A, period 1
    2         B                 1   # due to Ben being on B, period 1
    3         A                 1   # due to Ben being on A, period 2 
    3         B                 0   # no match from B, period 2

我知道 data.table 中的 .I 和 .GRP 运算符，但我不知道如何在语句的 j 条目中编写“下一组”的概念。我想像这样的事情可能是一条合理的路径，但我无法弄清楚正确的语法：

data[, .(recurrence_count = length(intersect(name, name[last(.GRP)]))), by = .(category, period)]