TCAModel(kernel_type='rbf', kernel_param=1.0, dim=20, mu=0.5)
Transfer Component Analysis (TCA) for domain adaptation.
TCA finds a latent space where source and target domain distributions are similar.
Parameters:
| Name | Type | Description | Default |
kernel_type | (linear, rbf, poly) | Type of kernel function to use: - 'linear': Linear kernel (dot product) - 'rbf': Radial Basis Function (Gaussian) kernel - 'poly': Polynomial kernel | 'linear' |
kernel_param | float | Parameter for kernel function: - For 'rbf': gamma parameter (inverse of kernel width) - For 'poly': degree of polynomial | 1.0 |
dim | int | Dimensionality of the latent space (number of components to keep) | 20 |
mu | float | Regularization parameter for numerical stability | 0.5 |
Attributes:
| Name | Type | Description |
W | ndarray of shape (n_samples, dim) or None | Learned transformation matrix. None before fitting. |
X_train | ndarray of shape (n_samples, n_features) or None | Training data stored for transformation. None before fitting. |
Source code in pydmoo/response/tca_model.py
| def __init__(self, kernel_type='rbf', kernel_param=1.0, dim=20, mu=0.5):
# For the TCA parameters, we set the Gaussian kernel function to the default value and the expected dimensionality
# was set to be 20. The value of μ was set to 0.5.
self.kernel_type = kernel_type
self.kernel_param = kernel_param
self.dim = dim
self.mu = mu
self.W = None
self.X_train = None
|
Functions
fit
Fit TCA model to source and target data.
Parameters:
| Name | Type | Description | Default |
Xs | ndarray of shape (ns_samples, n_features) | Source domain feature matrix | required |
Xt | ndarray of shape (nt_samples, n_features) | Target domain feature matrix | required |
Returns:
| Name | Type | Description |
self | object | Returns the instance itself. |
Source code in pydmoo/response/tca_model.py
| def fit(self, Xs, Xt):
"""Fit TCA model to source and target data.
Parameters
----------
Xs : ndarray of shape (ns_samples, n_features)
Source domain feature matrix
Xt : ndarray of shape (nt_samples, n_features)
Target domain feature matrix
Returns
-------
self : object
Returns the instance itself.
"""
# Stack source and target data vertically
X = np.vstack((Xs, Xt))
n = X.shape[0] # Total number of samples
ns, nt = Xs.shape[0], Xt.shape[0] # Number of source/target samples
# Compute kernel matrix K using selected kernel function
K = self._kernel(X, X)
self.X_train = X # Store for transform phase
# Construct MMD (Maximum Mean Discrepancy) matrix
# This matrix encodes the distribution difference between domains
M = np.zeros((n, n))
M[:ns, :ns] = 1/(ns*ns) # Source-source block
M[ns:, ns:] = 1/(nt*nt) # Target-target block
M[:ns, ns:] = M[ns:, :ns] = -1/(ns*nt) # Cross blocks
# Centering matrix H = I - 1/n * 11^T
# Projects data onto the space orthogonal to the vector of ones
H = np.eye(n) - np.ones((n, n))/n
# Solve generalized eigenvalue problem:
# (K(M)K + μI)^-1 K(H)K w = λw
# Using pseudo-inverse for numerical stability
A = np.linalg.pinv(K @ M @ K + self.mu*np.eye(n)) @ K @ H @ K
# Compute eigenvalues and eigenvectors
# eigh returns eigenvalues in ascending order
eigvals, eigvecs = eigh(A)
# Select top 'dim' eigenvectors corresponding to largest eigenvalues
# [::-1] reverses order to get descending eigenvalues
self.W = eigvecs[:, np.argsort(eigvals)[-self.dim:][::-1]]
return self
|
Transform data using learned TCA components.
Parameters:
| Name | Type | Description | Default |
X | ndarray of shape (n_samples, n_features) | | required |
Returns:
| Name | Type | Description |
X_transformed | ndarray of shape (n_samples, dim) | Data projected to the latent space |
Raises:
| Type | Description |
ValueError | If fit() hasn't been called before transform() |
Source code in pydmoo/response/tca_model.py
| def transform(self, X):
"""Transform data using learned TCA components.
Parameters
----------
X : ndarray of shape (n_samples, n_features)
Data to transform
Returns
-------
X_transformed : ndarray of shape (n_samples, dim)
Data projected to the latent space
Raises
------
ValueError
If fit() hasn't been called before transform()
"""
if self.W is None:
raise ValueError("Model not fitted yet. Call fit() first.")
# Compute kernel between new data and training data
K = self._kernel(X, self.X_train)
# Project to latent space: X' = K * W
return K @ self.W
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