evomap.mapping._optim#

Core functions shared within mapping module. Mostly related to different optimization routines implemented and adjusted for mapping.

Module Contents#

Functions#

gradient_descent_line_search(objective, init, n_iter)

Gradient descent with backtracking via halving.

gradient_descent_with_momentum(objective, init, n_iter)

Gradient descent with momentum.

report_optim_progress(iter, method_str, cost[, grad_norm])

Print optimization progress.

Attributes#

EPSILON

evomap.mapping._optim.EPSILON = 1e-12#
exception evomap.mapping._optim.Error[source]#

Bases: Exception

Base class for other exceptions

exception evomap.mapping._optim.DivergingGradientError[source]#

Bases: Error

Raised when the input value is too small

Gradient descent with backtracking via halving.

Optimizes the objective function iteratively. At each step, a halving procedure is used to ensure that step sizes are set such that cost values decrease.

Parameters

  • objective (callable) – Function to be optimized. Expected to return the function value and the gradient when called. See examples for exact syntax.

  • init (ndarray of shape (n_samples, n_dims)) – Starting initialization.

  • n_iter (int) – Total number of gradient descent iterations.

  • n_iter_check (int, optional) – Interval in which cost values are reported, by default 1

  • max_halves (int, optional) – Maximum number of halving steps in line search, by default 10

  • step_size (int, optional) – Initial step size, by default 1

  • min_grad_norm (float, optional) – Error tolerance, by default 1e-7

  • verbose (int, optional) – Level of verbosity, by default 0

  • method_str (str, optional) – Method label, by default “”

  • args (list, optional) – Arguments passed to the objective function, by default None

  • kwargs (dict, optional) – Keyword arguments passed to the objective function, by default None

Returns

  • ndarray of shape (n_samples, n_dims) – Final map coordinates

  • float – Final cost function value

evomap.mapping._optim.gradient_descent_with_momentum(objective, init, n_iter, start_iter=0, n_iter_check=50, momentum=0.8, eta=50, min_grad_norm=1e-07, verbose=0, method_str='', args=None, kwargs=None)[source]#

Gradient descent with momentum.

Optimize the objective function using momentum-based gradient descent, as used, for instance, in t-SNE.

Parameters

  • objective (callable) – Function to be optimized. Expected to return the function value and the gradient when called. See examples for exact syntax.

  • init (ndarray of shape (n_samples, n_dims)) – _description_

  • n_iter (int) – Total number of gradient descent iterations.

  • start_iter (int, optional) – Startint iteration, if optimization (re-)starts at a later stage , by default 0

  • n_iter_check (int, optional) – Interval in which cost values are reported, by default 50

  • momentum (float, optional) – Momentum factor, by default .8

  • eta (int, optional) – Learning rate, by default 50

  • min_grad_norm (float, optional) – Error tolerance, by default 1e-7

  • verbose (int, optional) – Level of verbosity, by default 0

  • method_str (str, optional) – Method label, by default “”

  • args (list, optional) – Arguments passed to the objective function, by default None

  • kwargs (dict, optional) – Keyword arguments passed to the objective function, by default None

Returns

  • ndarray of shape (n_samples, n_dims) – Final map coordinates

  • float – Final cost function value

evomap.mapping._optim.report_optim_progress(iter, method_str, cost, grad_norm=None)[source]#

Print optimization progress.

Parameters

  • iter (int) – Current iteration.

  • method_str (str) – Method label.

  • cost (float) – Current cost function value

  • grad_norm (float, optional) – Gradient norm, by default None