Method __init__

numpy_ml/factorization/factors.py:9–61

r""" Approximately factor a real-valued matrix using regularized alternating least-squares (ALS). Notes ----- The regularized ALS minimization problem is .. math:: \min_{\mathbf{W}, \mathbf{H}} ||\mathbf{X} - \mathbf{WH}||^2 -

(self, K, alpha=1, max_iter=200, tol=1e-4)

class VanillaALS:
    def __init__(self, K, alpha=1, max_iter=200, tol=1e-4):
        r"""
        Approximately factor a real-valued matrix using regularized alternating
        least-squares (ALS).

        Notes
        -----
        The regularized ALS minimization problem is

        .. math::

            \min_{\mathbf{W}, \mathbf{H}} ||\mathbf{X} - \mathbf{WH}||^2 -
                \alpha \left(
                    ||\mathbf{W}||^2 + ||\mathbf{H}||^2
                \right)

        where :math:`||\cdot||` denotes the Frobenius norm, **X** is the
        :math:`N \times M` data matrix, :math:`\mathbf{W}` and
        :math:`\mathbf{H}` are learned factor matrices with dimensions :math:`N
        \times K` and :math:`K \times M`, respectively, and :math:`\alpha` is a
        user-defined regularization weight.

        ALS proceeds by alternating between fixing **W** and optimizing for
        **H** and fixing **H** and optimizing for **W**. Vanilla ALS has no
        convergance guarantees and the objective function is prone to
        oscillation across updates, particularly for dense input matrices [1]_.

        References
        ----------
        .. [1] Gillis, N. (2014). The why and how of nonnegative matrix
           factorization.  *Regularization, optimization, kernels, and support
           vector machines, 12(257)*, 257-291.

        Parameters
        ----------
        K : int
            The number of latent factors to include in the factor matrices W
            and H.
        alpha : float
            The L2 regularization weight on the factor matrices. Larger
            values result in more aggressive regularization. Default is 1.
        max_iter : int
            The maximum number of iterations to run before stopping. Default is
            200.
        tol : float
            The tolerance for the stopping condition. Default is 1e-4.
        """
        self.K = K
        self.W = None
        self.H = None
        self.tol = tol
        self.alpha = alpha
        self.max_iter = max_iter

    @property
    def parameters(self):