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A package for Multiple Kernel Learning scikit-compliant

Project Description

MKLpy is a framework for Multiple Kernel Learning and kernel machines scikit-compliant.

This package contains:

  • MKL algorithms * EasyMKL * RM-GD * R-MKL * Average of kernels
  • a meta-MKL-classifier used in multiclass problems according to one-vs-one pattern;
  • tools to operate over kernels, such as normalization, centering, summation, mean…;
  • metrics, such as kernel_alignment, radius…;
  • kernel functions, such as HPK and boolean kernels (disjunctive, conjunctive, DNF, CNF).

For more informations about classification, kernels and predictors visit Link scikit-learn


To work properly, MKLpy requires:

  • numpy
  • scikit-learn
  • cvxopt



It is possible to load data by using scikit-learn, exploiting the svmlight standard

from sklearn.datasets import load_svmlight_file
X,Y = load_svmlight_file(path)
X = X.toarray() #Important! MKLpy require dense matrices!


MKLpy provides several tools to preprocess data, some examples are:

from MKLpy.regularization import normalization,rescale_01
X = rescale_01(X)
X = normalization(X)

It is also possible to operate on kernels directly

from MKLpy.metrics.pairwise import HPK_kernel
K = HPK_kernel(X,degree=2)

from MKLpy.regularization import          kernel_centering,           kernel_normalization,           tracenorm
Kc = kernel_centering(K)
Kn = kernel_normalization(K)
Kt = tracenorm(K)


MKL algorithms require list or arrays of kernels, it is possible to create any custom list

KL = [HPK_kernel(X,degree=d) for d in range(1,11)]

#creating lists of boolean kernels
from MKLpy.metrics.pairwise import              monotone_conjunctive_kernel as mCK,           monotone_disjunctive_kernel as mDK
#WARNING: boolean kernels require binary valued data {0,1}
KL = [mCK(X,k=d) for d in range(1,11)] + [mDK(X,k=d) for d in range(2,11)]


The learning phase consists on two steps: learning kernels and fit models by using a MKl algorithm and a standard kernel machine

from MKLpy.algorithms import EasyMKL,RMGD,RMKL,AverageMKL
#learn kernels
K_easy = EasyMKL(lam=0.1).arrange_kernel(KL,Y)
K_rmgd = RMGD(max_iter=3).arrange_kernel(KL,Y)
#fit models
from sklearn.svm import SVC
from MKLpy.algorithms import KOMD
clf_komd = KOMD(lam=0.1,kernel='precomputed').fit(K_easy,Y)
clf_svc  = SVC(C=10,kernel='precomputed').fit(K_rmgd,Y)

Now, we show a more suitable procedure, where MKL algorithms use a default base learner

clf = EasyMKL().fit(KL,Y)
clf = AverageMKL().fit(KL,Y)

It is also possible to set a custom base learner

clf = EasyMKL(estimator=SVC(C=1)).fit(KL,Y)


It is possible to evaluate a model by splitting a kernels list in train and test

from MKLpy.model_selection import train_test_split, cross_val_score
from sklearn.metrics import roc_auc_score

KLtr,KLte,Ytr,Yte = train_test_split(KL,Y,train_size=.75,random_state=42)
y_score =,Ytr).decision_function(KLte)
auc_score = roc_auc_score(Yte, y_score)

Or using a cross-validation procedure

clf = EasyMKL(estimator=SVC())
scores = cross_val_score(KL,Y,estimator=clf,n_folds=5)


MKLpy contains a wide set of tools for kernel learning and MKL, a simple example:

from MKLpy.metrics import margin, radius
K = AverageMKL().arrange_kernel(KL,Y)
rho = margin(K,Y) #distance between classes
R = radius(K) #radius of MEB
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