#-*- coding: utf8
# Author: David C. Lambert [dcl -at- panix -dot- com]
# Copyright(c) 2013
# License: Simple BSD
"""The :mod:`random_layer` module
implements Random Layer transformers.
Random layers are arrays of hidden unit activations that are
random functions of input activation values (dot products for simple
activation functions, distances from prototypes for radial basis
functions).
They are used in the implementation of Extreme Learning Machines (ELMs),
but can be used as a general input mapping.
"""
from abc import ABCMeta, abstractmethod
from math import sqrt
import numpy as np
import scipy.sparse as sp
from scipy.spatial.distance import cdist, pdist, squareform
from sklearn.metrics import pairwise_distances
from sklearn.utils import check_random_state, check_array #atleast2d_or_csr(X)
from sklearn.utils.extmath import safe_sparse_dot
from sklearn.base import BaseEstimator, TransformerMixin
__all__ = ['RandomLayer',
'MLPRandomLayer',
'RBFRandomLayer',
'GRBFRandomLayer',
]
class BaseRandomLayer(BaseEstimator, TransformerMixin):
"""Abstract Base Class for random layers"""
__metaclass__ = ABCMeta
_internal_activation_funcs = dict()
@classmethod
def activation_func_names(cls):
"""Get list of internal activation function names"""
return cls._internal_activation_funcs.keys()
# take n_hidden and random_state, init components_ and
# input_activations_
def __init__(self, n_hidden=20, random_state=0, activation_func=None,
activation_args=None):
self.n_hidden = n_hidden
self.random_state = random_state
self.activation_func = activation_func
self.activation_args = activation_args
self.components_ = dict()
self.input_activations_ = None
# keyword args for internally defined funcs
self._extra_args = dict()
@abstractmethod
def _generate_components(self, X):
"""Generate components of hidden layer given X"""
@abstractmethod
def _compute_input_activations(self, X):
"""Compute input activations given X"""
# compute input activations and pass them
# through the hidden layer transfer functions
# to compute the transform
def _compute_hidden_activations(self, X):
"""Compute hidden activations given X"""
self._compute_input_activations(X)
acts = self.input_activations_
if (callable(self.activation_func)):
args_dict = self.activation_args if (self.activation_args) else {}
X_new = self.activation_func(acts, **args_dict)
else:
func_name = self.activation_func
func = self._internal_activation_funcs[func_name]
X_new = func(acts, **self._extra_args)
return X_new
# perform fit by generating random components based
# on the input array
def fit(self, X, y=None):
"""Generate a random hidden layer.
Parameters
----------
X : {array-like, sparse matrix} of shape [n_samples, n_features]
Training set: only the shape is used to generate random component
values for hidden units
y : is not used: placeholder to allow for usage in a Pipeline.
Returns
-------
self
"""
X = check_array(X) #atleast2d_or_csr(X)
self._generate_components(X)
return self
# perform transformation by calling compute_hidden_activations
# (which will normally call compute_input_activations first)
def transform(self, X, y=None):
"""Generate the random hidden layer's activations given X as input.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
Data to transform
y : is not used: placeholder to allow for usage in a Pipeline.
Returns
-------
X_new : numpy array of shape [n_samples, n_components]
"""
X = check_array(X)#atleast2d_or_csr(X)
if (self.components_ is None):
raise ValueError('No components initialized')
return self._compute_hidden_activations(X)
class RandomLayer(BaseRandomLayer):
"""RandomLayer is a transformer that creates a feature mapping of the
inputs that corresponds to a layer of hidden units with randomly
generated components.
The transformed values are a specified function of input activations
that are a weighted combination of dot product (multilayer perceptron)
and distance (rbf) activations:
input_activation = alpha * mlp_activation + (1-alpha) * rbf_activation
mlp_activation(x) = dot(x, weights) + bias
rbf_activation(x) = rbf_width * ||x - center||/radius
alpha and rbf_width are specified by the user
weights and biases are taken from normal distribution of
mean 0 and sd of 1
centers are taken uniformly from the bounding hyperrectangle
of the inputs, and radii are max(||x-c||)/sqrt(n_centers*2)
The input activation is transformed by a transfer function that defaults
to numpy.tanh if not specified, but can be any callable that returns an
array of the same shape as its argument (the input activation array, of
shape [n_samples, n_hidden]). Functions provided are 'sine', 'tanh',
'tribas', 'inv_tribas', 'sigmoid', 'hardlim', 'softlim', 'gaussian',
'multiquadric', or 'inv_multiquadric'.
Parameters
----------
`n_hidden` : int, optional (default=20)
Number of units to generate
`alpha` : float, optional (default=0.5)
Mixing coefficient for distance and dot product input activations:
activation = alpha*mlp_activation + (1-alpha)*rbf_width*rbf_activation
`rbf_width` : float, optional (default=1.0)
multiplier on rbf_activation
`user_components`: dictionary, optional (default=None)
dictionary containing values for components that woud otherwise be
randomly generated. Valid key/value pairs are as follows:
'radii' : array-like of shape [n_hidden]
'centers': array-like of shape [n_hidden, n_features]
'biases' : array-like of shape [n_hidden]
'weights': array-like of shape [n_features, n_hidden]
`activation_func` : {callable, string} optional (default='tanh')
Function used to transform input activation
It must be one of 'tanh', 'sine', 'tribas', 'inv_tribas',
'sigmoid', 'hardlim', 'softlim', 'gaussian', 'multiquadric',
'inv_multiquadric' or a callable. If None is given, 'tanh'
will be used.
If a callable is given, it will be used to compute the activations.
`activation_args` : dictionary, optional (default=None)
Supplies keyword arguments for a callable activation_func
`random_state` : int, RandomState instance or None (default=None)
Control the pseudo random number generator used to generate the
hidden unit weights at fit time.
Attributes
----------
`input_activations_` : numpy array of shape [n_samples, n_hidden]
Array containing dot(x, hidden_weights) + bias for all samples
`components_` : dictionary containing two keys:
`bias_weights_` : numpy array of shape [n_hidden]
`hidden_weights_` : numpy array of shape [n_features, n_hidden]
See Also
--------
"""
# triangular activation function
_tribas = (lambda x: np.clip(1.0 - np.fabs(x), 0.0, 1.0))
# inverse triangular activation function
_inv_tribas = (lambda x: np.clip(np.fabs(x), 0.0, 1.0))
# sigmoid activation function
_sigmoid = (lambda x: 1.0/(1.0 + np.exp(-x)))
# hard limit activation function
_hardlim = (lambda x: np.array(x > 0.0, dtype=float))
_softlim = (lambda x: np.clip(x, 0.0, 1.0))
# gaussian RBF
_gaussian = (lambda x: np.exp(-pow(x, 2.0)))
# multiquadric RBF
_multiquadric = (lambda x:
np.sqrt(1.0 + pow(x, 2.0)))
# inverse multiquadric RBF
_inv_multiquadric = (lambda x:
1.0/(np.sqrt(1.0 + pow(x, 2.0))))
# internal activation function table
_internal_activation_funcs = {'sine': np.sin,
'tanh': np.tanh,
'tribas': _tribas,
'inv_tribas': _inv_tribas,
'sigmoid': _sigmoid,
'softlim': _softlim,
'hardlim': _hardlim,
'gaussian': _gaussian,
'multiquadric': _multiquadric,
'inv_multiquadric': _inv_multiquadric,
}
def __init__(self, n_hidden=20, alpha=0.5, random_state=None,
activation_func='tanh', activation_args=None,
user_components=None, rbf_width=1.0):
super(RandomLayer, self).__init__(n_hidden=n_hidden,
random_state=random_state,
activation_func=activation_func,
activation_args=activation_args)
if (isinstance(self.activation_func, str)):
func_names = self._internal_activation_funcs.keys()
if (self.activation_func not in func_names):
msg = "unknown activation function '%s'" % self.activation_func
raise ValueError(msg)
self.alpha = alpha
self.rbf_width = rbf_width
self.user_components = user_components
self._use_mlp_input = (self.alpha != 0.0)
self._use_rbf_input = (self.alpha != 1.0)
def _get_user_components(self, key):
"""Look for given user component"""
try:
return self.user_components[key]
except (TypeError, KeyError):
return None
def _compute_radii(self):
"""Generate RBF radii"""
# use supplied radii if present
radii = self._get_user_components('radii')
# compute radii
if (radii is None):
centers = self.components_['centers']
n_centers = centers.shape[0]
max_dist = np.max(pairwise_distances(centers))
radii = np.ones(n_centers) * max_dist/sqrt(2.0 * n_centers)
self.components_['radii'] = radii
def _compute_centers(self, X, sparse, rs):
"""Generate RBF centers"""
# use supplied centers if present
centers = self._get_user_components('centers')
# use points taken uniformly from the bounding
# hyperrectangle
if (centers is None):
n_features = X.shape[1]
if (sparse):
fxr = range(n_features)
cols = [X.getcol(i) for i in fxr]
min_dtype = X.dtype.type(1.0e10)
sp_min = lambda col: np.minimum(min_dtype, np.min(col.data))
min_Xs = np.array(map(sp_min, cols))
max_dtype = X.dtype.type(-1.0e10)
sp_max = lambda col: np.maximum(max_dtype, np.max(col.data))
max_Xs = np.array(map(sp_max, cols))
else:
min_Xs = X.min(axis=0)
max_Xs = X.max(axis=0)
spans = max_Xs - min_Xs
ctrs_size = (self.n_hidden, n_features)
centers = min_Xs + spans * rs.uniform(0.0, 1.0, ctrs_size)
self.components_['centers'] = centers
def _compute_biases(self, rs):
"""Generate MLP biases"""
# use supplied biases if present
biases = self._get_user_components('biases')
if (biases is None):
b_size = self.n_hidden
biases = rs.normal(size=b_size)
self.components_['biases'] = biases
def _compute_weights(self, X, rs):
"""Generate MLP weights"""
# use supplied weights if present
weights = self._get_user_components('weights')
if (weights is None):
n_features = X.shape[1]
hw_size = (n_features, self.n_hidden)
weights = rs.normal(size=hw_size)
self.components_['weights'] = weights
def _generate_components(self, X):
"""Generate components of hidden layer given X"""
rs = check_random_state(self.random_state)
if (self._use_mlp_input):
self._compute_biases(rs)
self._compute_weights(X, rs)
if (self._use_rbf_input):
self._compute_centers(X, sp.issparse(X), rs)
self._compute_radii()
def _compute_input_activations(self, X):
"""Compute input activations given X"""
n_samples = X.shape[0]
mlp_acts = np.zeros((n_samples, self.n_hidden))
if (self._use_mlp_input):
b = self.components_['biases']
w = self.components_['weights']
mlp_acts = self.alpha * (safe_sparse_dot(X, w) + b)
rbf_acts = np.zeros((n_samples, self.n_hidden))
if (self._use_rbf_input):
radii = self.components_['radii']
centers = self.components_['centers']
scale = self.rbf_width * (1.0 - self.alpha)
rbf_acts = scale * cdist(X, centers)/radii
self.input_activations_ = mlp_acts + rbf_acts
class MLPRandomLayer(RandomLayer):
"""Wrapper for RandomLayer with alpha (mixing coefficient) set
to 1.0 for MLP activations only"""
def __init__(self, n_hidden=20, random_state=None,
activation_func='tanh', activation_args=None,
weights=None, biases=None):
user_components = {'weights': weights, 'biases': biases}
super(MLPRandomLayer, self).__init__(n_hidden=n_hidden,
random_state=random_state,
activation_func=activation_func,
activation_args=activation_args,
user_components=user_components,
alpha=1.0)
class RBFRandomLayer(RandomLayer):
"""Wrapper for RandomLayer with alpha (mixing coefficient) set
to 0.0 for RBF activations only"""
def __init__(self, n_hidden=20, random_state=None,
activation_func='gaussian', activation_args=None,
centers=None, radii=None, rbf_width=1.0):
user_components = {'centers': centers, 'radii': radii}
super(RBFRandomLayer, self).__init__(n_hidden=n_hidden,
random_state=random_state,
activation_func=activation_func,
activation_args=activation_args,
user_components=user_components,
rbf_width=rbf_width,
alpha=0.0)
class GRBFRandomLayer(RBFRandomLayer):
"""Random Generalized RBF Hidden Layer transformer
Creates a layer of radial basis function units where:
f(a), s.t. a = ||x-c||/r
with c the unit center
and f() is exp(-gamma * a^tau) where tau and r are computed
based on [1]
Parameters
----------
`n_hidden` : int, optional (default=20)
Number of units to generate, ignored if centers are provided
`grbf_lambda` : float, optional (default=0.05)
GRBF shape parameter
`gamma` : {int, float} optional (default=1.0)
Width multiplier for GRBF distance argument
`centers` : array of shape (n_hidden, n_features), optional (default=None)
If provided, overrides internal computation of the centers
`radii` : array of shape (n_hidden), optional (default=None)
If provided, overrides internal computation of the radii
`use_exemplars` : bool, optional (default=False)
If True, uses random examples from the input to determine the RBF
centers, ignored if centers are provided
`random_state` : int or RandomState instance, optional (default=None)
Control the pseudo random number generator used to generate the
centers at fit time, ignored if centers are provided
Attributes
----------
`components_` : dictionary containing two keys:
`radii_` : numpy array of shape [n_hidden]
`centers_` : numpy array of shape [n_hidden, n_features]
`input_activations_` : numpy array of shape [n_samples, n_hidden]
Array containing ||x-c||/r for all samples
See Also
--------
ELMRegressor, ELMClassifier, SimpleELMRegressor, SimpleELMClassifier,
SimpleRandomLayer
References
----------
.. [1] Fernandez-Navarro, et al, "MELM-GRBF: a modified version of the
extreme learning machine for generalized radial basis function
neural networks", Neurocomputing 74 (2011), 2502-2510
"""
# def _grbf(acts, taus):
# """GRBF activation function"""
# return np.exp(np.exp(-pow(acts, taus)))
_grbf = (lambda acts, taus: np.exp(np.exp(-pow(acts, taus))))
_internal_activation_funcs = {'grbf': _grbf}
def __init__(self, n_hidden=20, grbf_lambda=0.001,
centers=None, radii=None, random_state=None):
super(GRBFRandomLayer, self).__init__(n_hidden=n_hidden,
activation_func='grbf',
centers=centers, radii=radii,
random_state=random_state)
self.grbf_lambda = grbf_lambda
self.dN_vals = None
self.dF_vals = None
self.tau_vals = None
# get centers from superclass, then calculate tau_vals
# according to ref [1]
def _compute_centers(self, X, sparse, rs):
"""Generate centers, then compute tau, dF and dN vals"""
super(GRBFRandomLayer, self)._compute_centers(X, sparse, rs)
centers = self.components_['centers']
sorted_distances = np.sort(squareform(pdist(centers)))
self.dF_vals = sorted_distances[:, -1]
self.dN_vals = sorted_distances[:, 1]/100.0
#self.dN_vals = 0.0002 * np.ones(self.dF_vals.shape)
tauNum = np.log(np.log(self.grbf_lambda) /
np.log(1.0 - self.grbf_lambda))
tauDenom = np.log(self.dF_vals/self.dN_vals)
self.tau_vals = tauNum/tauDenom
self._extra_args['taus'] = self.tau_vals
# get radii according to ref [1]
def _compute_radii(self):
"""Generate radii"""
denom = pow(-np.log(self.grbf_lambda), 1.0/self.tau_vals)
self.components_['radii'] = self.dF_vals/denom
