1、电影评分数据集
load ('ex8_movies.mat');
该数据集包含两个矩阵，分别是矩阵Y和矩阵R，其维度均为1682943（ij）。
Y(i,j)表示为第j个用户对第i个电影的评分，R中数据为0或1,R(i,j) = 1表示为第j个用户对第i个电影有评分，0表示为未评分。
若需要对第1部电影的已有评分计算其平均分，则代码应为：
mean(Y(1, R(1, :)));
数据可视化图形为：
J = sum(sum(((X*Theta' - Y).*R).^2))/2;
运行得：
Cost at loaded parameters: 22.224604
(this value should be about 22.22)
2.2、协同过滤梯度
X_grad = R.*(X*Theta' - Y)*Theta ;
Theta_grad = (R.*(X*Theta' - Y))'*X
运行程序得：
Checking Gradients (without regularization) ...
5.5335 5.5335
3.6186 3.6186
5.4422 5.4422
-1.7312 -1.7312
4.1196 4.1196
-1.4833 -1.4833
-6.0734 -6.0734
2.3490 2.3490
7.6341 7.6341
1.8651 1.8651
4.1192 4.1192
-1.5834 -1.5834
1.2828 1.2828
-6.1573 -6.1573
1.6628 1.6628
1.1686 1.1686
5.5630 5.5630
0.3050 0.3050
4.42 4.42
-1.6691 -1.6691
-2.1505 -2.1505
-3.6832 -3.6832
3.4067 3.4067
-4.0743 -4.0743
0.5567 0.5567
-2.1056 -2.1056
0.9168 0.9168
The above two columns you get should be very similar.
(Left-Your Numerical Gradient, Right-Analytical Gradient)
If your cost function implementation is correct, then
the relative difference will be small (less than 1e-9).
Relative Difference: 1.84952e-12
2.3、正则化损失函数
J = sum(sum((R.*(X*Theta' - Y)).^2))/2 + sum(sum(Theta.^2))*lambda/2+...
sum(sum(X.^2))*lambda/2;
2.4、正则化梯度
J = sum(sum((R.*(X*Theta' - Y)).^2))/2 + sum(sum(Theta.^2))*lambda/2+...
sum(sum(X.^2))*lambda/2;
X_grad = R.*(X*Theta' - Y)*Theta + X*lambda;
Theta_grad = (R.*(X*Theta' - Y))'*X + Theta*lambda;
运行程序有：
Cost at loaded parameters (lambda = 1.5): 31.344056
(this value should be about 31.34)
Checking Gradients (with regularization) ...
2.2223 2.2223
0.7968 0.7968
-3.2924 -3.2924
-0.7029 -0.7029
-4.2016 -4.2016
3.5969 3.5969
0.8859 0.8859
1.0523 1.0523
-7.8499 -7.8499
0.3904 0.3904
-0.1347 -0.1347
-2.3656 -2.3656
2.1066 2.1066
1.6703 1.6703
0.8519 0.8519
-1.0380 -1.0380
2.6537 2.6537
0.8114 0.8114
-0.8604 -0.8604
-0.5884 -0.5884
-0.7108 -0.7108
-4.0652 -4.0652
0.2494 0.2494
-4.3484 -4.3484
-3.6167 -3.6167
-4.1277 -4.1277
-3.2439 -3.2439
The above two columns you get should be very similar.
(Left-Your Numerical Gradient, Right-Analytical Gradient)
If your cost function implementation is correct, then
the relative difference will be small (less than 1e-9).
Relative Difference: 1.701e-12
3.电影推荐系统
New user ratings:
Rated 4 for Toy Story (1995)
Rated 3 for Twelve Monkeys (1995)
Rated 5 for Usual Suspects, The (1995)
Rated 4 for Outbreak (1995)
Rated 5 for Shawshank Redemption, The (1994)
Rated 3 for While You Were Sleeping (1995)
Rated 5 for Forrest Gump (1994)
Rated 2 for Silence of the Lambs, The (1991)
Rated 4 for Alien (1979)
Rated 5 for Die Hard 2 (1990)
Rated 5 for Sphere (1998)
Program paused. Press enter to continue.
Training collaborative filtering...
Iteration 1 | Cost: 3.108511e+05
Iteration 2 | Cost: 1.475959e+05
Iteration 3 | Cost: 1.000321e+05
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Iteration 100 | Cost: 3.7217e+04
Recommender system learning completed.
Program paused. Press enter to continue.
Top recommendations for you:
Predicting rating 5.0 for movie Saint of Fort Washington, The (1993)
Predicting rating 5.0 for movie Great Day in Harlem, A (1994)
Predicting rating 5.0 for movie Someone Else's America (1995)
Predicting rating 5.0 for movie Entertaining Angels: The Dorothy Day Story (1996)
Predicting rating 5.0 for movie Santa with Muscles (1996)
Predicting rating 5.0 for movie Aiqing wansui (1994)
Predicting rating 5.0 for movie Prefontaine (1997)
Predicting rating 5.0 for movie They Made Me a Criminal (1939)
Predicting rating 5.0 for movie Marlene Dietrich: Shadow and Light (1996)
Predicting rating 5.0 for movie Star Kid (1997)
Original ratings provided:
Rated 4 for Toy Story (1995)
Rated 3 for Twelve Monkeys (1995)
Rated 5 for Usual Suspects, The (1995)
Rated 4 for Outbreak (1995)
Rated 5 for Shawshank Redemption, The (1994)
Rated 3 for While You Were Sleeping (1995)
Rated 5 for Forrest Gump (1994)
Rated 2 for Silence of the Lambs, The (1991)
Rated 4 for Alien (1979)
Rated 5 for Die Hard 2 (1990)
Rated 5 for Sphere (1998)
