Calculator Inputs
Example Data Table
| Row \ Col | C1 | C2 | C3 | C4 |
|---|---|---|---|---|
| R1 | 9 | 7 | — | 6 |
| R2 | 8 | — | 6 | 5 |
| R3 | — | 6 | 5 | — |
| R4 | 6 | 5 | — | 3 |
In this example, blank positions are estimated from observed structure. You can compare simpler mean fills against the low-rank iterative option.
Formula Used
1. Global mean fill
x̂ij = x̄obs
2. Row mean fill
x̂ij = average of observed values in row i
3. Column mean fill
x̂ij = average of observed values in column j
4. Two-way mean fill
x̂ij = (row mean + column mean) / 2, with fallback to the available mean or global mean
5. Low-rank iterative SVD
Start with a basic filled matrix, compute a rank-r approximation, keep original observed cells fixed, replace only missing cells, and iterate until the largest change falls below the chosen tolerance.
How to Use This Calculator
- Choose the number of rows and columns.
- Pick a completion method.
- Enter known matrix values and leave missing cells blank.
- Set rank, iteration count, and tolerance if using low-rank completion.
- Click Complete Matrix to estimate all missing values.
- Review the summary, colored matrix, and Plotly charts.
- Download the completed results as CSV or PDF.
Frequently Asked Questions
1) What does matrix completion mean here?
This calculator estimates blank matrix entries from the observed values. It supports simple mean-based approaches and an iterative low-rank approximation for more structured statistical tables.
2) When should I use the low-rank method?
Use low-rank completion when your data likely has shared hidden structure, such as correlated rows and columns. It is often more informative than raw averages for patterned matrices.
3) What rank should I choose?
Start with rank 1 or 2 for small matrices. Lower ranks impose stronger structure, while higher ranks fit more detail. Compare outputs and use the most reasonable result.
4) Can I enter negative values or decimals?
Yes. The calculator accepts integers, decimals, and negative numbers. Only blank cells are treated as missing values to be estimated.
5) Why do different methods give different answers?
Each method encodes a different assumption. Mean fills rely on local averages, while low-rank completion assumes the full matrix can be described using fewer latent dimensions.
6) Does this tool change observed cells?
No. Observed entries remain fixed. Only blank cells are estimated, especially in the iterative low-rank method where the known values anchor the reconstruction.
7) What does the heatmap show?
The heatmap visualizes the completed matrix values. It helps you spot gradients, clusters, and unusual cells after imputation, making the completed structure easier to interpret.
8) Is this suitable for production research work?
It is useful for screening, education, and quick analysis. For critical research decisions, validate assumptions, compare methods, and document why the selected completion rule fits your data.