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.

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.

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

Internal variables of interest

self.avg

Mean of the input data (available after training)

self.v

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

Instance Methods

[hide private]

__init__(self, input_dim=None, output_dim=None, dtype=None)
If the input dimension and the output dimension are unspecified, they will be set when the train or execute method is called for the first time. If dtype is unspecified, it will be inherited from the data it receives at the first call of train or execute.

_check_train_args(self, x, labels)

_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.

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 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.

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)

If the input dimension and the output dimension are unspecified, they will be set when the train or execute method is called for the first time. If dtype is unspecified, it will be inherited from the data it receives at the first call of train or execute.

Every subclass must take care of up- or down-casting the internal structures to match this argument (use _refcast private method when possible).

Overrides: object.__init__: (inherited documentation)

_check_train_args(self, x, labels)

Overrides: Node._check_train_args

_execute(self, x, n=None)

Compute the output of the FDA projection.

If 'n' is an integer, then use the first 'n' components.

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'.

x -- a matrix having different variables on different columns: and observations on the rows.
label -- 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

_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.

x -- Data points from a single class. label -- The label for that class.

_update_means(self, x, label)

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

x -- Data points from a single class. label -- The label for that class.

execute(self, x, n=None)

Compute the output of the FDA projection.

If 'n' is an integer, then use the first 'n' components.

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'.

x -- a matrix having different variables on different columns: and observations on the rows.
label -- 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

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)

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