ADV Kernel — Adaptive Density Variance Kernel

A scikit-learn compatible SVM kernel that adapts its bandwidth sample-by-sample using two complementary signals:

The final kernel is a pointwise product of an adaptive RBF and a polynomial term:

K(xᵢ, xⱼ) = exp(−‖xᵢ−xⱼ‖² / 2σᵢσⱼ) × (1 + β⟨xᵢ,xⱼ⟩)^degree

Installation

pip install adv-kernel

Or directly from GitHub:

pip install git+https://github.com/InquietoPartho/adv_kernel.git

Quick start

from adv_kernel import ADVKernelSVC

clf = ADVKernelSVC(C=1.0, beta=0.5, degree=2, probability=True)
clf.fit(X_train, y_train)

y_pred  = clf.predict(X_test)
y_proba = clf.predict_proba(X_test)

Use kernel functions directly

from adv_kernel import adv_bandwidth, adv_kernel

sigma = adv_bandwidth(X, k=10, gamma_density=1.0, gamma_var=0.5)
K     = adv_kernel(X, X, sigma, sigma, beta=0.5, degree=2)

scikit-learn GridSearchCV

from sklearn.model_selection import GridSearchCV
from adv_kernel import ADVKernelSVC

param_grid = {"C": [0.1, 1.0, 10.0], "beta": [0.2, 0.5], "gamma_density": [0.5, 1.0]}
gs = GridSearchCV(ADVKernelSVC(), param_grid, cv=5, n_jobs=-1)
gs.fit(X_train, y_train)
print(gs.best_params_)

API reference

adv_bandwidth(X, k=10, gamma_density=1.0, gamma_var=0.5)

Returns per-sample bandwidth array of shape (n_samples,).

adv_kernel(X, Y, sigma_X, sigma_Y, beta=0.5, degree=2)

Returns kernel matrix of shape (n_X, n_Y).

ADVKernelSVC parameters

License

MIT © Pijush Kanti Roy Partho