adv-kernel 0.1.0

Adaptive Density Variance (ADV) Kernel — a locally-adaptive hybrid RBF×Polynomial kernel for scikit-learn SVMs

ADV Kernel — Adaptive Density Variance Kernel

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

Signal	Meaning
k-NN density	Sparse neighbourhood → wider kernel
Feature variance	High intra-sample heterogeneity → wider kernel

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

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Installation

pip install adv-kernel

Or directly from GitHub:

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

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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_)

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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

Parameter	Default	Description
C	1.0	SVM regularisation
beta	0.5	Polynomial scaling
degree	2	Polynomial degree
k_bw	10	k-NN neighbours for bandwidth
gamma_density	1.0	Density term weight
gamma_var	0.5	Variance term weight
probability	True	Enable predict_proba

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License

MIT © Pijush Kanti Roy Partho