def get_trajectory(self, **kwargs):
r"""
Returns the currently computed trajectory.
INPUT:
- ``self`` -- ``Observer`` object on which the function is invoked.
- ``observable`` -- ``Observable`` whose status has changed.
- ``plotter`` -- ``Plotter`` object (default: automatically detects a
running sage or matplotlib environment) to be used in order to
render graphics.
The function forwards other options affecting the graphics style to
the ``list_plot`` function of the specified or detected plotter.
OUTPUT:
No output.
EXAMPLES:
See ``ErrorTrajectory``.
AUTHORS:
- Dario Malchiodi (2010-02-22)
"""
try:
plotter = kwargs['plotter']
del kwargs['plotter']
except KeyError:
#if detect_sage():
# plotter = SagePlotter()
#else:
# plotter = MatplotlibPlotter()
plotter = PlotterFactory.get_plotter()
return plotter.list_plot(zip(self.trajectory_time, \
self.trajectory_value), **kwargs)
def plot(self, ranges, **kwargs):
r"""
Returns the plot SV classifier decision function. Depending on the
environment within which the function is called, the plot is returned
as a matplotlib figure or as a sage graphics. Raises a ValueError if
invoked on classifiers not having exactly two or three input units.
The SV classifier decision function plot can contain: i) the plot of
the curve/surface separating positive and negative patterns, ii) the
plot of the curve/surface corresponding to SV margin, and iii) a color
gradient describing the decision function values. The appearance of
all these ingredients is customizable through the ``plot`` function
named arguments.
INPUT:
- ``self`` -- SVMClassifier object on which the function is invoked.
- ``args`` -- list of two or three visualization ranges for the
involved variables, where each range is in turn a two-elements list
or tuple containing respectively the lower and upper extreme.
- ``separator`` -- boolean (default value: True) flag triggering the
visualization of the curve/surface separating positive and negative
patterns.
- ``separator_color`` -- color (default value: 'black') color to be
used in order to draw the curve/surface separating positive and
negative patterns.
- ``separator_style`` -- line style (default value: '-') style to be
used in order to draw the curve/surface separating positive and
negative patterns.
- ``separator_width`` -- number (default value: 1) line width to be
used in order to draw the curve/surface separating positive and
negative patterns.
- ``margin`` -- boolean (default value: False) flag triggering the
visualization of the curve/surface showing the SV margin.
- ``margin_color`` -- color (default value: 'gray') color to be used
in order to draw the curve/surface showing the SV margin.
- ``margin_style`` -- line style (default value: '-') style to be used
in order to draw the curve/surface showing the SV margin.
- ``margin_width`` -- number (default value: 1) line width to be used
in order to draw the curve/surface showing the SV margin.
- ``shading`` -- boolean (default value: False) flag triggering the
decision function visualization in form of a color gradient.
- ``shading_color`` -- colormap (default value: Greys) colormap to be
used in order to show decision function values.
- ``plotter`` -- Plotter object (default: SagePlotter() when the code
is run within sage and MatplotlibPlotter() otherwise) to be used in
order to render graphics.
OUTPUT:
graphic object -- the decision function plot, in form of a matplotlib
figure or of a sage graphic.
EXAMPLES:
Consider the following ``SVMClassifier`` instance expressly tailored in
order to deal with the binary AND sample:
::
>>> from yaplf.data import LabeledExample
>>> from yaplf.models.svm import SVMClassifier
>>> and_sample = [LabeledExample((1., 1.), 1.),
... LabeledExample((0., 0.), -1.), LabeledExample((0, 1), -1.),
... LabeledExample((1, 0), -1.)]
>>> svc = SVMClassifier([3, 1, 1, 1], -3, and_sample)
The first arguments to ``plot`` are the visualization ranges. In this
case two such ranges are needed, for the SV classifier has two inputs.
In the following example, the visualization range is `(0, 1.7)^2` and
the plot will contain a red separator and show the SV margin (colored
in gray as this is the default choice):
::
>>> svc.plot((0., 1.7), (0., 1.7), separator_color = 'red',
... margin = True)
The above function call automatically detects the environment it is
invoked into, returning either a sage graphics or a matplotlib figure.
It is anyway possible to force a specific return value through
specification of the ``plotter`` named argument. For instance, the
following instruction explicitly require to use matplotlib, and this
allows for specific line styles not (yet?) supported in the default
sage graphics library:
::
>>> from yaplf.graph import MatplotlibPlotter
>>> fig = svc.plot((0., 1.7), (0., 1.7),
... plotter = MatplotlibPlotter(), separator_color = 'red',
... separator_style = '--', margin = True, margin_width = 3,
... color_bar = True)
>>> fig.savefig('and-SVC.png')
It is important to point out that the above function call can be used
within sage, too. Moreover, when using the notebook facility instead
of the command line interface, invocation of the ``savefig`` function
has the effect of showing up the plot in the notebook. The matplotlib
plotter is used within sage when particular features not (yet?)
implemented are needed in a plot, such as particular line styles.
Using a specific kernel function instead of the default one
corresponding to a standard dot product in the original patterns space
requires to refer to the named argument ``kernel``, whose valid values
are specific subinstances of the ``Kernel`` class defined in package
yaplf.utility. For instance, the following instructions build an
instance of ``SVClassifier`` expressly tailored in order to correctly
classify a binary XOR sample through exploitation of a Gaussian kernel,
subsequently plotting its decision function in `(0, 2)^2` and showing
both separator and margin:
::
>>> from yaplf.models.kernel import GaussianKernel
>>> xor_sample = [LabeledExample((1., 1.), -1.),
... LabeledExample((0., 0.), -1.), LabeledExample((0, 1), 1.),
... LabeledExample((1, 0), 1.)]
>>> svc = SVMClassifier([6.21, 6.21, 6.71, 6.71], -0.65,
... xor_sample, kernel = GaussianKernel(1))
>>> svc.plot((0., 2.), (0., 2.), margin = True)
The same result can be obtained through specific plotters, such as
those based on matplotlib:
::
>>> fig = svc.plot((0., 2.), (0., 2.), margin = True,
... plotter = MatplotlibPlotter())
>>> fig.savefig('mpl-gauss-svm.png')
Plots can be combined easily in sage through the graph concatenation
operator `+`. The following example shows how to plot a data set
together with the corresponding SV classifier decision function:
::
>>> from yaplf.data import classification_data_plot
>>> cf = lambda x: ('white' if x.label == 1 else 'red')
>>> fig_xor_sample = classification_data_plot(xor_sample,
... color_function = cf)
>>> svc = SVMClassifier([1.52, 2.02, 2.02, 1.52], -0.39,
... xor_sample, kernel = GaussianKernel(0.6))
>>> fig_xor_model = svc.plot((-1, 2), (-1, 2), margin = True,
... separator = True, shading = True, margin_color = 'red')
>>> fig_xor_model + fig_xor_sample
A similar result in matplotlib requires the use of ``base`` named
argument:
::
>>> fig_mpl = classification_data_plot(xor_sample,
... color_function = cf, plotter = MatplotlibPlotter())
>>> fig_mpl = svc.plot((-1, 2), (-1, 2), margin = True,
... separator = True, shading = True, margin_color = 'red',
... margin_style = ":", plotter = MatplotlibPlotter(),
... base = fig_mpl)
>>> fig_mpl.savefig('mpl-svm-xor.png')
The figure produced by ``plot`` can be fine tuned. For instance, the
following instructions produce a decision function plot of another SV
classifier for the binary XOR function, where the curve highlighting
the SV margin is rendered through a red dashed style with fixed line
width, while the gradient is colored in blue shades:
::
>>> from matplotlib.cm import Blues
>>> svc = SVMClassifier([0.5, 1, 1, 0.5], -0.76, xor_sample,
... kernel = GaussianKernel(0.5))
>>> fig_xor_model_color = svc.plot((-.9, 1.9), (-.9, 1.9),
... margin = True, separator = True, shading = True,
... margin_color = 'red', margin_width = 1, margin_style = '--',
... shading_color = Blues)
>>> fig_xor_model_color + fig_xor_sample
A similar result can be obtained through matplotlib exploiting the
same technique previously explained:
::
>>> fig_mpl_2 = classification_data_plot(xor_sample,
... color_function = cf, plotter = MatplotlibPlotter())
>>> fig_mpl_2 = svc.plot((-.9, 1.9), (-.9, 1.9), margin = True,
... separator = True, shading = True, margin_color = 'red',
... margin_width = 1, margin_style = '--', shading_color = Blues,
... plotter = MatplotlibPlotter(), base = fig_mpl_2,
... color_bar = True)
>>> fig_mpl_2.savefig('mpl-svm-xor-color.png')
Decision function plots are available also for SV classifiers having
three inputs, although with a limited number of features:
::
>>> td_sample = [LabeledExample((1., 1., 1.), 1),
... LabeledExample((0., 0., 1.), -1),
... LabeledExample((0., 1, 0.), -1),
... LabeledExample((1., 0., 0.), -1),
... LabeledExample((0., 0., 0.), 1)]
>>> p0 = classification_data_plot(td_sample,
... color_function = lambda x: ('green' if x.label == 1 else
... 'yellow'))
... svc = SVMClassifier([11.04, 10.42, 10.42, 10.42, 21.24],
... -1.14, td_sample, kernel = GaussianKernel(1.4))
>>> p1 = svc.plot((-.5, 3.), (-1., 3.), (-1., 3.))
>>> p0 + p1
AUTHORS:
- Dario Malchiodi (2010-02-22)
"""
try:
separator = kwargs["separator"]
del kwargs["separator"]
except KeyError:
separator = True
try:
separator_color = kwargs["separator_color"]
del kwargs["separator_color"]
except KeyError:
separator_color = "black"
try:
separator_style = kwargs["separator_style"]
del kwargs["separator_style"]
except KeyError:
separator_style = "-"
try:
separator_width = kwargs["separator_width"]
del kwargs["separator_width"]
except KeyError:
separator_width = 1
try:
margin = kwargs["margin"]
del kwargs["margin"]
except KeyError:
margin = False
try:
margin_color = kwargs["margin_color"]
del kwargs["margin_color"]
except KeyError:
margin_color = "gray"
try:
margin_style = kwargs["margin_style"]
del kwargs["margin_style"]
except KeyError:
margin_style = "-"
try:
margin_width = kwargs["margin_width"]
del kwargs["margin_width"]
except KeyError:
margin_width = 1
try:
shading = kwargs["shading"]
del kwargs["shading"]
except KeyError:
shading = False
try:
shading_color = kwargs["shading_color"]
del kwargs["shading_color"]
except KeyError:
shading_color = Greys
levels = []
levels_color = []
levels_style = []
levels_width = []
if margin:
levels.append(-1.0)
levels_color.append(margin_color)
levels_style.append(margin_style)
levels_width.append(margin_width)
if separator:
levels.append(0.0)
levels_color.append(separator_color)
levels_style.append(separator_style)
levels_width.append(separator_width)
if margin:
levels.append(1.0)
levels_color.append(margin_color)
levels_style.append(margin_style)
levels_width.append(margin_width)
kwargs["contours"] = levels
kwargs["contour_color"] = levels_color
kwargs["contour_style"] = levels_style
kwargs["contour_width"] = levels_width
kwargs["gradient"] = shading
kwargs["gradient_color"] = shading_color
try:
plotter = kwargs["plotter"]
del kwargs["plotter"]
except KeyError:
plotter = PlotterFactory.get_plotter()
return plotter.decision_function_plot(ranges, lambda x, y: self.classifier.decision_function((x, y)), **kwargs)
def plot(self, *args, **kwargs):
r"""
Returns a graphic containing the plot of the perceptron output. Raises
a ValueError if invoked on perceptrons not having two or three input
units. The graphic is either a bi- or three-dimensional plot according
to the following invocation syntax:
- ``plot(x_range, y_range)`` returns a 2D plot.
- ``plot(x_range, y_range, z_range)`` returns a 3D plot.
INPUT:
- ``self`` -- ``Perceptron`` object on which the function is invoked.
- ``x_range`` -- bidimensional iterable containing the range of x
variable.
- ``y_range`` -- bidimensional iterable containing the range of y
variable.
- ``z_range`` -- bidimensional iterable containing the range of z
variable.
- ``shading`` -- boolean (default value: False) flag triggering the
perceptron output visualization in form of a color gradient.
- ``shading_color`` -- colormap (default value: Greys) colormap to be
used in order to show perceptron output.
- ``x_points`` -- integer (default: 50 in 2D, 35 in 3D) number of
samples in x range.
- ``y_points`` -- integer (default: 50 in 2D, 35 in 3D) number of
samples in y range.
- ``z_points`` -- integer (default: 50 in 2D, 35 in 3D) number of
samples in z range.
- ``output`` -- integer (default: unused) output to be selected when
drawing the decision function if the perceptron has several output
units, not specified when the perceptron has one output unit.
- ``base`` -- matplotlib figure (default: a new figure) figure to be
used to draw the decision function.
- ``contours``-- iterable of numeric values (default: empty tuple)
perceptron output values to be highlighted through contours.
- ``contour_color`` -- iterable of colors or single color value
(default: 'gray') colors of the drawn contours; if a single value is
supplied, it refers to all contours.
- ``contour_width`` -- iterable of numberic values or single numeric
value (default: 1) width of the drawn contours; if a single numeric
value is supplied, it refers to all contours.
- ``contour_style`` -- iterable or single value of a valid style
(default: '-') style of the drawn contours; if a single value is
supplied, it refers to all contours.
- ``color_bar`` -- boolean (default: False) flag setting the
visualization of a color legend.
- ``plotter`` -- Plotter object (default: SagePlotter() when the code
is run within sage and MatplotlibPlotter() otherwise) to be used in
order to render graphics.
OUTPUT:
graphic object -- the perceptron output values plot in function of
possible input values, in form of a matplotlib figure or of a sage
graphic.
EXAMPLES:
Another way to visualize a perceptron's behaviour is through the
``plot`` function, generating a graphic object summarizing the outputs
for a given range of possible inputs:
::
>>> from yaplf.utility.activation import SigmoidActivationFunction
>>> from yaplf.models.neural import Perceptron
>>> p = Perceptron(((4, 4),), threshold = (6,),
... activation = SigmoidActivationFunction(0.8))
>>> p.plot((-5, 5), (-5, 5), plot_points = 100,
... contours = (0.1, 0.5, 0.9),
... contour_color = ('red', 'green', 'blue'), shading = True)
Here the first two arguments represent the ranges for the possible
values for the two perceptron input units, and the obtained graph
contains a colored gradient shading from white to black in order to
visualize how the perceptron output varies w.r.t. the possible input
values (named argument ``shading``), highlighting through colored
curves specific output values (where named arguments ``contours`` and
``contour_color`` specify these values and the color of the
corresponding curves, while ``plot_points`` refers to the precision to
be used in order to approximate those curves through a set of
successive segments).
Only perceptrons having two or three inputs allow invocation of the
``plot`` function. In the second case it will be necessary to specify
three input value ranges, and the result will be a 3D graph:
::
>>> p = Perceptron(((.3, 9.56, .2),), threshold=(1.7,),
... activation = SigmoidActivationFunction(beta = .1))
>>> p.plot((-5, 5), (-5, 5), (-5, 5), plot_points = 20,
... contours=(0.1, 0.5, 0.9), contour_color = ('red', 'green',
... 'blue'), shading = True)
AUTHORS:
- Dario Malchiodi (2010-02-22)
"""
if not 1 < self.perceptron.get_num_inputs() < 4:
raise ValueError('plot only works for 2-inputs and 3-inputs \
perceptrons.')
if len(args) != self.perceptron.get_num_inputs():
raise ValueError('plot ranges incompatible with perceptron \
inputs.')
try:
shading = kwargs['shading']
del kwargs['shading']
except KeyError:
shading = False
try:
shading_color = kwargs['shading_color']
del kwargs['shading_color']
except KeyError:
shading_color = Greys
kwargs['gradient'] = shading
kwargs['gradient_color'] = shading_color
try:
output_unit = kwargs['output']
def classify(*args):
"""Classification function created on-the-fly."""
return self.perceptron.decision_function(args)[output_unit]
except KeyError:
def classify(*args):
"""Classification function created on-the-fly."""
return self.perceptron.decision_function(args)
try:
plotter = kwargs['plotter']
del kwargs['plotter']
except KeyError:
plotter = PlotterFactory.get_plotter()
return plotter.decision_function_plot(args, classify, **kwargs)