如何在 Matlab 中矢量化搜索功能？

Question

这是一个 Matlab 编码问题（与 intersect not setdiff here 略有不同的版本：

一个有3列的评分矩阵A，第1列是可能重复的用户ID，第2列是可能重复的项目ID，第3列是用户对项目的评分，范围从1到5。

现在，我有一个用户 ID 子集 smallUserIDList 和一个项目 ID 子集 smallItemIDList，然后我想在 smallUserIDList 中找到 A 中用户评分的行，并收集用户评分的项目，并进行一些计算，例如 setdiff with smallItemIDList 并计算结果，如下代码所示：

userStat = zeros(length(smallUserIDList), 1);
for i = 1:length(smallUserIDList)
    A2= A(A(:,1) == smallUserIDList(i), :);
    itemIDList_each = unique(A2(:,2));

    setDiff = setdiff(itemIDList_each , smallItemIDList);
    userStat(i) = length(setDiff);
end
userStat

最后，我发现配置文件查看器显示上面的循环效率低下，问题是如何通过矢量化而不是 for 循环的帮助来改进这段代码？

例如：

输入：

A = [
1 11 1
2 22 2
2 66 4
4 44 5
6 66 5
7 11 5
7 77 5
8 11 2
8 22 3
8 44 3
8 66 4
8 77 5    
]

smallUserIDList = [1 2 7 8]
smallItemIDList = [11 22 33 55 77]

输出：

userStat =

 0
 1
 0
 2

Answer 1

原版 MATLAB：

据我所知，您的代码相当于：

%// Create matrix such that: user_item_rating(user,item)==rating
user_item_rating = sparse(A(:,1),A(:,2),A(:,3));

%// Keep all BUT the items in smallItemIDList
user_item_rating(:,smallItemIDList) = [];

%// Keep only those users in `smallUserIDList` and use order of this list
user_item_rating = user_item_rating(smallUserIDList,:);

%// Count the number of ratings
userStat = sum(user_item_rating~=0, 2);

如果每个(user,item)-combination 最多有一个评级，这将起作用。而且效率应该很高。

干净的方法，无需重新发明轮子：

从统计工具箱中查看grpstats！ 实现可能类似于：

%// Create ratings table
ratings = array2table(A, 'VariableNames', {'user','item','rating'});

%// Remove items we don't care about (smallItemIDList)
ratings = ratings(~ismember(ratings.item, smallItemIDList),:);

%// Keep only users we care about (smallUserIDList) 
ratings = ratings(ismember(ratings.user, smallUserIDList),:);

%// Compute the statistics grouped by 'user'. 
userStat = grpstats(ratings, 'user');

Answer 2

这可能是一种vectorized 方法-

%// Take care of equality between first column of A and smallUserIDList to 
%// find the matching row and column indices.
%// NOTE: This corresponds to "A(:,1) == smallUserIDList(i)" from OP.
[R,C] = find(bsxfun(@eq,A(:,1),smallUserIDList.')); %//'

%// Take care of non-equality between second column of A and smallItemIDList. 
%// NOTE: This corresponds to SETDIFF in the original loopy code from OP.
mask1 = ~ismember(A(R,2),smallItemIDList);

AR2 = A(R,2); %// Elements from 2nd col of A that has matches from first step

%// Get only those elements from C and AR2 that has ONES in mask1
C1 = C(mask1);
AR2 = AR2(mask1);

%// Initialized output array
userStat = zeros(numel(smallUserIDList),1);

if ~isempty(C1)%//There is at least one element in C, so do further processing
    
    %// Find the count of duplicate elements for each ID in C1 indexed into AR2.
    %// NOTE: This corresponds to "unique(A2(:,2))" from OP.
    dup_counts = accumarray(C1,AR2,[],@(x) numel(x)-numel(unique(x)));
    
    %// Get the count of matches for each ID in C in the mask1.
    %// NOTE: This corresponds to:
    %//       "length(setdiff(itemIDList_each , smallItemIDList))" from OP.
    accums = accumarray(C,mask1);
    
    %// Store the counts in output array and also subtract the dup counts
    userStat(1:numel(accums)) = accums;
    userStat(1:numel(dup_counts)) = userStat(1:numel(dup_counts)) - dup_counts;
end

---

基准测试

接下来列出的代码将建议方法的运行时与原始循环代码进行比较 -

%// Size parameters and random inputs with them
A_nrows    = 5000;
IDlist_len = 5000;
max_userID = 1000;
max_itemID = 1000;
A = [randi(max_userID,A_nrows,1) randi(max_itemID,A_nrows,1) randi(5,A_nrows,2)];
smallUserIDList = randi(max_userID,IDlist_len,1);
smallItemIDList = randi(max_itemID,IDlist_len,1);

disp('---------------------------- With Original Approach')
tic
%//   Original posted code
toc

disp('---------------------------- With Proposed Approach'))
tic
%//   Proposed approach code
toc

因此使用三组数据大小获得的运行时间是 -

案例#1：

A_nrows    = 500;
IDlist_len = 500;
max_userID = 100;
max_itemID = 100;
---------------------------- With Original Approach
Elapsed time is 0.136630 seconds.
---------------------------- With Proposed Approach
Elapsed time is 0.004163 seconds.

案例#2：

A_nrows    = 5000;
IDlist_len = 5000;
max_userID = 100;
max_itemID = 100;
---------------------------- With Original Approach
Elapsed time is 1.579468 seconds.
---------------------------- With Proposed Approach
Elapsed time is 0.050498 seconds.

案例#3：

A_nrows    = 5000;
IDlist_len = 5000;
max_userID = 1000;
max_itemID = 1000;
---------------------------- With Original Approach
Elapsed time is 1.252294 seconds.
---------------------------- With Proposed Approach
Elapsed time is 0.044198 seconds.

结论：因此，所提出的方法对原始循环代码的加速似乎是巨大的！

Answer 3

我认为您正在尝试为一部分用户删除一组固定的评分并计算剩余评分的数量：

做以下工作：

Asub = A(ismember(A(:,1), smallUserIDList),1:2);
Bremove = allcomb(smallUserIDList, smallItemIDList);
Akeep = setdiff(Asub, Bremove, 'rows');
T = varfun(@sum, array2table(Akeep), 'InputVariables', 'Akeep2', 'GroupingVariables', 'Akeep1');
% userStat = T.GroupCount;

你需要来自 matlab 中心的文件交换的 allcomb 函数，它给出了两个向量的笛卡尔积，而且很容易实现。