非负矩阵分解中的评分预测 [英] Rating prediction in non negative matrix factorization

问题描述

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然后，我们应用MF算法，以创建一个新的矩阵R'，该矩阵是2个矩阵P(UxK)和Q(DxK)的乘积.然后，我们将R和R'中给出的值的误差最小化".到目前为止，效果很好.但是，在最后一步中，当矩阵被填满时，我不太相信这些是用户将给出的预测值.这是最终的矩阵:

证明这些实际上是预测的"评级的依据是什么?另外，我计划将P矩阵(UxK)用作用户的潜在功能.我们可以以某种方式证明"这些是用户的潜在功能吗?

解决方案

将每个用户获得的向量用作潜在特征向量的理由是，使用这些潜在潜在特征的值将最小化预测收视率与实际已知收视率之间的误差.

如果您在发布的两个图中查看预测的收视率和已知的收视率，您会发现两者共同的单元格中的两个矩阵之间的差异非常小.示例:U1D4在第一个图中为1，在第二个图中为0.98.

由于特征或用户潜在特征向量在已知等级上产生良好的结果，因此我们认为在预测未知等级上会做得很好.当然，我们使用正则化来避免过度拟合训练数据，但这是总的想法.

I was following this blog http://www.quuxlabs.com/blog/2010/09/matrix-factorization-a-simple-tutorial-and-implementation-in-python/ (Also attaching the matrix here)for the rating prediction using matrix factorization . Initially we have a sparse user-movie matrix R .

We then apply the MF algorithm so as to create a new matrix R' which is the product of 2 matrix P(UxK) and Q(DxK) . We then "minimize" the error in the value given in R and R' .So far so good . But in the final step , when the matrix is filled up , I am not so convinced that these are the predicted values that the user will give . Here is the final matrix:

What is the basis of justification that these are in fact the "predicted" ratings . Also , I am planning to use the P matrix (UxK) as the user's latent features . Can we somehow "justify" that these are infact user's latent features ?

解决方案

The justification for using the obtained vectors for each user as latent trait vectors is that using these values of the latent latent traits will minimize the error between the predicted ratings and the actual known ratings.

If you take a look at the predicted ratings and the known ratings in the two diagrams that you posted you can see that the difference between the two matrixes in the cells that are common to both is very small. Example: U1D4 is 1 in the first diagram and 0.98 in the second.

Since the features or user latent trait vector produces good results on the known ratings we think that it would do a good job on predicting the unknown ratings. Of course, we use regularisation to avoid overfitting the training data, but that is the general idea.

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