Calculator Inputs
Formula Used
The dot product measures vector similarity. Gamma scales that similarity. The coefficient shifts the polynomial base before exponentiation.
Set the coefficient to zero for homogeneous mode. Positive values create inhomogeneous polynomial kernels. Higher degrees can magnify small parameter changes quickly.
How to Use
- Select a calculation mode.
- Enter vectors or dataset rows.
- Choose degree, gamma, and coefficient.
- Select optional preprocessing and precision.
- Calculate, inspect, compare, or export results.
Example Data
| Input | Example | Purpose |
|---|---|---|
| Vector X | 1, 2 | First feature vector |
| Vector Y | 3, 4 | Second feature vector |
| Gamma | 1 | Scales the dot product |
| Coefficient | 1 | Adds an independent offset |
| Degree | 2 | Controls polynomial complexity |
| Kernel value | 144 | (1 × 11 + 1)² |
Frequently Asked Questions
What is a polynomial kernel?
It measures similarity using a powered polynomial transformation. This avoids explicitly creating every expanded feature. It is commonly used with support vector machines.
What does degree control?
Degree controls the polynomial transformation complexity. Larger degrees model stronger feature interactions. They can also increase instability and overfitting risk.
What does gamma control?
Gamma scales the dot product before exponentiation. Larger gamma values amplify similarity differences. Small changes may strongly affect high-degree results.
What is the independent coefficient?
The coefficient shifts the base before exponentiation. Zero creates a homogeneous polynomial kernel. Nonzero values add lower-order interaction terms.
What does gamma auto mean?
Auto gamma equals one divided by feature count. This provides a simple dimension-based setting. It matches a common machine learning convention.
What does gamma scale mean?
Scale gamma also considers input variance. It divides one by features times variance. Zero variance makes this option undefined.
Why can results become extremely large?
Exponentiation magnifies the polynomial base rapidly. High degrees and gamma values increase growth. Use scaling and moderate parameters for stability.
What is a Gram matrix?
A Gram matrix contains pairwise kernel values. Its rows and columns represent observations. Polynomial kernel matrices are symmetric by construction.
Can vectors contain negative values?
Yes, negative feature values are supported. Their dot product may also become negative. Integer degrees determine the final sign behaviour.