Package mdp :: Package nodes :: Class FDANode

Class FDANode

Perform a (generalized) Fisher Discriminant Analysis of its input. It is a supervised node that implements FDA using a generalized eigenvalue approach.

Note: FDANode has two training phases and is supervised so make sure to pay attention to the following points when you train it: - call the ``train`` method with *two* arguments: the input data and the labels (see the doc string of the ``train`` method for details). - if you are training the node by hand, call the ``train`` method twice. - if you are training the node using a flow (recommended), the only argument to ``Flow.train`` must be a list of ``(data_point, label)`` tuples or an iterator returning lists of such tuples, *not* a generator. The ``Flow.train`` function can be called just once as usual, since it takes care of *rewinding* the iterator to perform the second training step.

Reference

More information on Fisher Discriminant Analysis can be found for example in C. Bishop, Neural Networks for Pattern Recognition, Oxford Press, pp. 105-112.

Instance Methods

[hide private]

__init__(self, input_dim=None, output_dim=None, dtype=None)
Initializes an object of type 'FDANode'.

_check_train_args(self, x, labels)

numpy.ndarray

_execute(self, x, n=None)
Compute the output of the FDA projection.

_get_train_seq(self)

_inverse(self, y)

_stop_fda(self)
Solve the eigenvalue problem for the total covariance.

_stop_means(self)
Calculate the class means.

_train(self, x, label)
Update the internal structures according to the input data 'x'.

_train_fda(self, x, labels)
Gather data for the overall and within-class covariance

_train_means(self, x, labels)
Gather data to compute the means and number of elements.

_update_SW(self, x, label)
Update the covariance matrix of the class means.

_update_means(self, x, label)
Update the internal variables that store the data for the means.

numpy.ndarray

execute(self, x, n=None)
Compute the output of the FDA projection.

inverse(self, y)
Invert y.

train(self, x, label)
Update the internal structures according to the input data 'x'.

Inherited from unreachable.newobject: __long__, __native__, __nonzero__, __unicode__, next

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Inherited from Node

__add__(self, other)

__call__(self, x, *args, **kwargs)
Calling an instance of Node is equivalent to calling its execute method.

__repr__(self)
repr(x)

__str__(self)
str(x)

_check_input(self, x)

_check_output(self, y)

_get_supported_dtypes(self)
Return the list of dtypes supported by this node.

_if_training_stop_training(self)

_pre_execution_checks(self, x)
This method contains all pre-execution checks.

_pre_inversion_checks(self, y)
This method contains all pre-inversion checks.

_refcast(self, x)
Helper function to cast arrays to the internal dtype.

_set_dtype(self, t)

_set_input_dim(self, n)

_set_output_dim(self, n)

_stop_training(self, *args, **kwargs)

copy(self, protocol=None)
Return a deep copy of the node.

get_current_train_phase(self)
Return the index of the current training phase.

get_dtype(self)
Return dtype.

get_input_dim(self)
Return input dimensions.

get_output_dim(self)
Return output dimensions.

get_remaining_train_phase(self)
Return the number of training phases still to accomplish.

get_supported_dtypes(self)
Return dtypes supported by the node as a list of numpy.dtype objects.

has_multiple_training_phases(self)
Return True if the node has multiple training phases.

is_training(self)
Return True if the node is in the training phase, False otherwise.

save(self, filename, protocol=-1)
Save a pickled serialization of the node to filename. If filename is None, return a string.

set_dtype(self, t)
Set internal structures' dtype.

set_input_dim(self, n)
Set input dimensions.

set_output_dim(self, n)
Set output dimensions.

stop_training(self, *args, **kwargs)
Stop the training phase.

Static Methods

[hide private]

Inherited from Node

is_invertible()
Return True if the node can be inverted, False otherwise.

is_trainable()
Return True if the node can be trained, False otherwise.

Instance Variables

[hide private]

avg
Mean of the input data (available after training).

v
Transposed of the projection matrix, so that output = dot(input-self.avg, self.v) (available after training).

Properties

[hide private]

Inherited from object: __class__

Inherited from Node

_train_seq
List of tuples:

dtype
dtype

input_dim
Input dimensions

output_dim
Output dimensions

supported_dtypes
Supported dtypes

Method Details

[hide private]

init(self, input_dim=None, output_dim=None, dtype=None)
(Constructor)

Initializes an object of type 'FDANode'.

Parameters:

input_dim (int) - The input dimensionality.
output_dim (int) - The output dimensionality.
dtype (numpy.dtype or str) - The datatype.

Overrides: object.__init__

_check_train_args(self, x, labels)

Overrides: Node._check_train_args

_execute(self, x, n=None)

Compute the output of the FDA projection.

Parameters:

x (numpy.ndarray) - Data to project.
n (int) - If 'n' is a positive integer, then use the first 'n' components. Otherwise use all.

Returns: numpy.ndarray

The output of the FDA projection.

Overrides: Node._execute

_get_train_seq(self)

Overrides: Node._get_train_seq

_inverse(self, y)

Overrides: Node._inverse

_stop_fda(self)

Solve the eigenvalue problem for the total covariance.

_stop_means(self)

Calculate the class means.

_train(self, x, label)

Update the internal structures according to the input data 'x'.

Parameters:

x (numpy.ndarray) - A matrix having different variables on different columns and observations on the rows.
label (list, tuple, numpy.ndarray or int) - Can be a list, tuple or array of labels (one for each data point) or a single label, in which case all input data is assigned to the same class.

Overrides: Node._train

_train_fda(self, x, labels)

Gather data for the overall and within-class covariance

Parameters:

x (numpy.ndarray) - Data points from classes specified by labels.
labels (int, list, tuple or numpy.ndarray) - Labels of the data points.

_train_means(self, x, labels)

Gather data to compute the means and number of elements.

Parameters:

x (numpy.ndarray) - The data.
labels (list, tuple, numpy.ndarray) - The class labels.

_update_SW(self, x, label)

Update the covariance matrix of the class means.

Parameters:

x (numpy.ndarray) - Data points from a single class.
label (int) - The label for the specific class.

_update_means(self, x, label)

Update the internal variables that store the data for the means.

Parameters:

x (numpy.ndarray) - Data points from a single class.
label (int) - The label for that class.

execute(self, x, n=None)

Compute the output of the FDA projection.

Parameters:

x (numpy.ndarray) - Data to project.
n (int) - If 'n' is a positive integer, then use the first 'n' components. Otherwise use all.

Returns: numpy.ndarray

The output of the FDA projection.

Overrides: Node.execute

inverse(self, y)

Invert y.

If the node is invertible, compute the input x such that y = execute(x).

By default, subclasses should overwrite _inverse to implement their inverse function. The docstring of the inverse method overwrites this docstring.

Overrides: Node.inverse

train(self, x, label)

Update the internal structures according to the input data 'x'.

Parameters:

x (numpy.ndarray) - A matrix having different variables on different columns and observations on the rows.
label (list, tuple, numpy.ndarray or int) - Can be a list, tuple or array of labels (one for each data point) or a single label, in which case all input data is assigned to the same class.

Overrides: Node.train

Instance Variable Details

[hide private]

avg

Mean of the input data (available after training).

v

Transposed of the projection matrix, so that output = dot(input-self.avg, self.v) (available after training).

Class FDANode

__init__(self, input_dim=None, output_dim=None, dtype=None) (Constructor)

_check_train_args(self, x, labels)

_execute(self, x, n=None)

_get_train_seq(self)

_inverse(self, y)

_stop_fda(self)

_stop_means(self)

_train(self, x, label)

_train_fda(self, x, labels)

_train_means(self, x, labels)

_update_SW(self, x, label)

_update_means(self, x, label)

execute(self, x, n=None)

inverse(self, y)

train(self, x, label)

avg

v

init(self, input_dim=None, output_dim=None, dtype=None)
(Constructor)