Isolation Distribution Kernel

ikpykit.kernel.IsoDisKernel

IsoDisKernel(
    method="anne",
    n_estimators=200,
    max_samples="auto",
    random_state=None,
)

Bases: BaseEstimator, TransformerMixin

Isolation Distributional Kernel is a new way to measure the similarity between two distributions.

It addresses two key issues of kernel mean embedding, where the kernel employed has: (i) a feature map with intractable dimensionality which leads to high computational cost; and (ii) data independency which leads to poor detection accuracy in anomaly detection.

Parameters:

Name	Type	Description	Default
method	str	The method to compute the isolation kernel feature. The available methods are: anne, inne, and iforest.	"anne"
n_estimators	int	The number of base estimators in the ensemble.	200
max_samples	int	The number of samples to draw from X to train each base estimator. - If int, then draw `max_samples` samples. - If float, then draw `max_samples` * X.shape[0]` samples. - If "auto", then `max_samples=min(8, n_samples)`.	"auto"
random_state	int, RandomState instance or None	Controls the pseudo-randomness of the selection of the feature and split values for each branching step and each tree in the forest. Pass an int for reproducible results across multiple function calls. See :term:Glossary <random_state>.	None

References

.. [1] Kai Ming Ting, Bi-Cun Xu, Takashi Washio, and Zhi-Hua Zhou. 2020. "Isolation Distributional Kernel: A New Tool for Kernel based Anomaly Detection". In Proceedings of the 26^th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD '20). Association for Computing Machinery, New York, NY, USA, 198-206.

Examples:

>>> from ikpykit.kernel import IsoDisKernel
>>> import numpy as np
>>> X = [[0.4,0.3], [0.3,0.8], [0.5,0.4], [0.5,0.1]]
>>> idk = IsoDisKernel(max_samples=3,).fit(X)
>>> D_i = [[0.4,0.3], [0.3,0.8]]
>>> D_j = [[0.5, 0.4], [0.5, 0.1]]
>>> idk.similarity(D_j, D_j)
1.0

Source code in ikpykit/kernel/_isodiskernel.py

def __init__(
    self, method="anne", n_estimators=200, max_samples="auto", random_state=None
) -> None:
    self.n_estimators = n_estimators
    self.max_samples = max_samples
    self.random_state = random_state
    self.method = method

fit

fit(X)

Fit the model on data X.

Parameters:

Name	Type	Description	Default
X	np.array of shape (n_samples, n_features)	The input instances.	required

Returns:

Name	Type	Description
self	object

Source code in ikpykit/kernel/_isodiskernel.py

def fit(self, X):
    """Fit the model on data X.
    Parameters
    ----------
    X : np.array of shape (n_samples, n_features)
        The input instances.
    Returns
    -------
    self : object
    """
    X = check_array(X)
    iso_kernel = IsoKernel(
        self.method, self.n_estimators, self.max_samples, self.random_state
    )
    self.iso_kernel_ = iso_kernel.fit(X)
    self.is_fitted_ = True
    return self

kernel_mean

kernel_mean(X)

Compute the kernel mean embedding of X.

Source code in ikpykit/kernel/_isodiskernel.py

def kernel_mean(self, X):
    """Compute the kernel mean embedding of X."""
    if sp.issparse(X):
        return np.asarray(X.mean(axis=0)).ravel()
    return np.mean(X, axis=0)

similarity

similarity(D_i, D_j, is_normalize=True)

Compute the isolation distribution kernel of D_i and D_j.

Parameters:

Name	Type	Description	Default
D_i		The input instances.	required
D_j		The input instances.	required
is_normalize			True

Returns:

Type	Description
The Isolation distribution similarity of given two dataset.

Source code in ikpykit/kernel/_isodiskernel.py

def similarity(self, D_i, D_j, is_normalize=True):
    """Compute the isolation distribution kernel of D_i and D_j.
    Parameters
    ----------
    D_i: array-like of shape (n_instances, n_features)
        The input instances.
    D_j: array-like of shape (n_instances, n_features)
        The input instances.
    is_normalize: whether return the normalized similarity matrix ranged of [0,1]. Default: False
    Returns
    -------
    The Isolation distribution similarity of given two dataset.
    """
    emb_D_i, emb_D_j = self.transform(D_i, D_j)
    kme_D_i, kme_D_j = self.kernel_mean(emb_D_i), self.kernel_mean(emb_D_j)
    return self.kme_similarity(kme_D_i, kme_D_j, is_normalize=is_normalize)

transform

transform(D_i, D_j)

Compute the isolation kernel feature of D_i and D_j.

Parameters:

Name	Type	Description	Default
D_i		The input instances.	required
D_j		The input instances.	required

Returns:

Type	Description
The finite binary features based on the kernel feature map.
The features are organised as a n_instances by psi*t matrix.

Source code in ikpykit/kernel/_isodiskernel.py

def transform(self, D_i, D_j):
    """Compute the isolation kernel feature of D_i and D_j.
    Parameters
    ----------
    D_i: array-like of shape (n_instances, n_features)
        The input instances.
    D_j: array-like of shape (n_instances, n_features)
        The input instances.
    Returns
    -------
    The finite binary features based on the kernel feature map.
    The features are organised as a n_instances by psi*t matrix.
    """
    check_is_fitted(self)
    D_i = check_array(D_i)
    D_j = check_array(D_j)
    return self.iso_kernel_.transform(D_i), self.iso_kernel_.transform(D_j)