Enter Ratings and Options
Use a responsive 3-column, 2-column, and 1-column calculator layout.
Example Data Table
This sample matrix shows observed ratings and missing entries represented by 0.
| User / Item | Movie A | Movie B | Movie C | Movie D | Movie E | Movie F |
|---|---|---|---|---|---|---|
| Alice | 5 | 3 | 0 | 1 | 4 | 0 |
| Bob | 4 | 0 | 0 | 1 | 4 | 2 |
| Carla | 1 | 1 | 0 | 5 | 0 | 4 |
| Dan | 0 | 0 | 5 | 4 | 0 | 5 |
| Eva | 2 | 1 | 3 | 0 | 0 | 4 |
Formula Used
SVD factorizes the prepared ratings matrix into orthogonal user and item patterns:
A truncated recommender keeps only the top k singular values:
If user-mean centering is enabled, the final prediction restores the user baseline:
Reconstruction quality on observed cells is summarized with root mean squared error:
How to Use This Calculator
- Paste a user-item rating matrix into the ratings box.
- Keep missing ratings as 0, NA, or your chosen token.
- Optionally enter user and item labels for readable outputs.
- Choose the number of latent factors, fill strategy, and rating scale.
- Select a target user and item index for focused prediction.
- Submit the form to calculate recommendations and reconstructed scores.
- Review the summary cards, recommendation table, and singular-value graph.
- Download the result section as CSV or PDF for reporting.
FAQs
1) What does the latent factor value k control?
It controls how many compressed preference dimensions the model keeps. Smaller values smooth the matrix more. Larger values preserve detail but can also capture noise from sparse or inconsistent ratings.
2) Why are zeros treated as missing values?
In recommendation problems, a zero often means no rating was given. Treating zeros as missing prevents the model from assuming a user explicitly disliked every unrated item.
3) Can this calculator recommend items a user has never rated?
Yes. The top recommendation list is built from items missing for the chosen user. Those scores come from the reconstructed matrix after factorization and optional baseline restoration.
4) Why would I enable user-mean centering?
Centering reduces bias from users who consistently rate high or low. It helps the decomposition focus on relative taste patterns instead of raw scoring habits alone.
5) What happens when the matrix is very sparse?
Predictions become more sensitive to the fill strategy, chosen factor count, and available overlap between users and items. Try fewer factors and compare RMSE or recommendation stability.
6) Is this the same as a production streaming recommender?
No. This is a compact educational and analytical calculator for small matrices. Production systems usually add regularization, temporal behavior, implicit feedback, and scalable training pipelines.
7) Why clip predictions to the rating scale?
Truncated matrix reconstruction can create values outside the original rating bounds. Clipping keeps predictions easier to interpret when your source data uses a strict scale such as 1 to 5.
8) When should I use item-mean filling instead of user-mean filling?
Item means work well when items have stronger global popularity patterns. User means fit cases where rating habits differ more by person than by item.