[英]Is there a heuristic algorithm for groupBy + count?
I got a List of integers and I want to count the number of times each integer appears in the list.我有一个整数列表,我想计算每个整数出现在列表中的次数。
For example: [0,5,0,1,3,3,1,1,1]
gives (0 -> 2), (1 -> 4), (3 -> 2), (5 -> 1)
.例如:
[0,5,0,1,3,3,1,1,1]
给出(0 -> 2), (1 -> 4), (3 -> 2), (5 -> 1)
. I only need the count, not the value (the goal is to have an histogram of the counts).我只需要计数,而不是值(目标是获得计数的直方图)。
A common approach would be to group by value then count the cardinality of each set.一种常见的方法是按值分组,然后计算每个集合的基数。 In SQL:
SELECT count(*) FROM myTable GROUPBY theColumnContainingIntegers
.在 SQL 中:
SELECT count(*) FROM myTable GROUPBY theColumnContainingIntegers
。
Is there a faster way to do this?有没有更快的方法来做到这一点? A heuristic or a probabilistic approach is fine since I am computing a large data set and sacrifying precision for speed is fine.
启发式或概率方法很好,因为我正在计算大型数据集并且为了速度而牺牲精度很好。
Something similar to HyperLogLog algorithm (used to count the number of distinct elements in a data set) would be great, but I did not find anything like this...类似于 HyperLogLog 算法(用于计算数据集中不同元素的数量)的东西会很棒,但我没有找到这样的东西......
Let's take your set containing 9 elements [0,5,0,1,3,3,1,1,1]
and make it big but with same frequencies of elements:让我们将包含 9 个元素
[0,5,0,1,3,3,1,1,1]
集合设为大但元素频率相同:
> bigarray = [0,5,0,1,3,3,1,1,1] * 200
=> [0, 5, 0, 1, 3, 3, 1, 1, 1, 0, 5, 0, 1, 3, 3, 1, ...
Now bigarray size is 1800 so let's try to work with it.现在 bigarray 大小为 1800,所以让我们尝试使用它。
Take a sample of 180 elements (random 180 elements from this set)取 180 个元素的样本(从这个集合中随机抽取 180 个元素)
Now compute occurence for this random subset现在计算这个随机子集的出现
{5=>19, 3=>45, 1=>76, 0=>40}
Normalized:标准化:
{5=>1.0, 3=>2.3684210526315788, 1=>4.0, 0=>2.1052631578947367}
Of course for different random subset results will be different:当然对于不同的随机子集结果会有所不同:
{5=>21, 3=>38, 1=>86, 0=>35}
Normalized归一化
{5=>1.0, 3=>1.8095238095238095, 1=>4.095238095238095, 0=>1.6666666666666667}
Of course there are some errors there - this is inevitable and you will need to state what will be acceptable error当然,那里有一些错误 - 这是不可避免的,您需要说明可接受的错误
Now make same test for bigarray (size 1000) with 50% of 0's and 50% of 1's现在用 50% 的 0 和 50% 的 1 对 bigarray(大小 1000)进行相同的测试
> bigarray = [0,1] * 500
=> [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...
With sample of 100 elements:使用 100 个元素的样本:
{0=>50, 1=>50}
Normalized归一化
{0=>1.0, 1=>1.0}
Second sample:第二个样本:
{0=>49, 1=>51}
Normalized归一化
{0=>1.0, 1=>1.0408163265306123}
It seems that we can easily reduce our subset and here Sampling comes.似乎我们可以轻松地减少我们的子集,采样就来了。
Especially Reservoir Sampling - this may be very useful if in your case data is populated 'live' or set is too large to process all values at once.尤其是Reservoir Sampling - 如果在您的情况下数据填充为“实时”或集合太大而无法一次处理所有值,这可能非常有用。
edit编辑
Concerning comment: Of course if you have large set and some element appears there very rare then you may have lost it and occurence will equal 0.关于评论:当然,如果你有一个很大的集合并且一些元素出现在那里非常罕见,那么你可能已经丢失了它并且出现将等于 0。
Then you may use kind of smoothing function (check additive smoothing ).然后你可以使用一种平滑功能(检查附加平滑)。 Just assume that each possible element 1 more time than it really appeared.
假设每个可能的元素比实际出现的时间多 1 次。
For example let's say we have set:例如,假设我们已经设置:
1000 elements 1
100 elements 2
10 elements 3
1 elements 4
Let's say our subset contains {1=>100,2=>10,3=>1, 4=>0}假设我们的子集包含 {1=>100,2=>10,3=>1, 4=>0}
Smoothing param = 0.05 so we add 0.05 to each occurence平滑参数 = 0.05 所以我们为每次出现添加 0.05
{1=>100.05,2=>10.05,3=>1.05, 4=>0.05} {1=>100.05,2=>10.05,3=>1.05, 4=>0.05}
Of course this is assuming that you know what values are even possible to be present in the set.当然,这是假设您知道集合中甚至可能存在哪些值。
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