Estimate embedding dimension from sampled series data. Review neighbor behavior, delay settings, and reconstructed vectors. Improve nonlinear analysis with practical outputs today.
| Index | Observed Value | Delay | Candidate Dimension |
|---|---|---|---|
| 1 | 2.10 | 1 | 2 |
| 2 | 2.50 | 1 | 3 |
| 3 | 3.00 | 1 | 4 |
| 4 | 3.80 | 1 | 5 |
| 5 | 4.90 | 1 | 6 |
This calculator uses the False Nearest Neighbors method. A scalar time series is reconstructed into vectors:
Y(i) = [x(i), x(i+τ), x(i+2τ), ..., x(i+(m-1)τ)]
Here, τ is the delay and m is the embedding dimension. For each point in dimension m, the nearest neighbor is found. Then the same pair is checked in dimension m+1.
A neighbor is marked false when the extra coordinate expands too much:
R = |x(i+mτ) - x(j+mτ)| / Dm
If R exceeds the relative threshold, or the expanded distance becomes too large compared with the series deviation, the neighbor is false. The suggested dimension is the first dimension where the false-neighbor percentage drops below the chosen target.
Embedding dimension helps rebuild hidden system dynamics from one measured signal. It supports phase space reconstruction for nonlinear analysis. A low dimension can fold trajectories together. A high dimension can add noise and computation. Good estimation improves forecasting, attractor study, and state-space modeling.
The False Nearest Neighbors method checks whether close points remain close after one more delayed coordinate is added. If many neighbors separate strongly, the current dimension is too small. When the percentage falls, the geometry becomes more reliable. This makes the method practical for measured scientific and engineering series.
Delay controls how far apart coordinates are in reconstructed vectors. Very small delays can create redundant coordinates. Very large delays can destroy structure. Thresholds affect sensitivity. Stricter thresholds may suggest higher dimensions. Softer thresholds may reduce recommended dimensions. Analysts should test values that match signal noise and sampling quality.
This calculator reports false-neighbor percentages across tested dimensions. It also gives a suggested embedding dimension based on a target limit. The preview table shows reconstructed vectors for quick inspection. Use these results with domain knowledge, especially for noisy, short, or strongly nonstationary signals. Recheck settings before making final modeling decisions.
It is the number of delayed coordinates used to reconstruct a state space from one observed time series. It helps reveal the system structure.
It is a point that looks close in a low dimension but separates after adding another coordinate. That indicates under-embedding.
Delay sets the spacing between coordinates in each reconstructed vector. It strongly affects redundancy and geometric separation.
Many users start with 5% or less. The right target depends on noise level, sample size, and analysis purpose.
Normalization helps when values have large magnitudes or scale shifts. It can improve threshold interpretation and numerical stability.
Euclidean is the most common default. Manhattan and Chebyshev can be useful when you want different sensitivity to coordinate differences.
Short series reduce usable vectors and weaken nearest-neighbor testing. Results may become unstable or insufficient for higher dimensions.
No. It is a strong screening tool, but final dimension choice should also consider signal quality, delay selection, and domain context.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.