From deb0d23c6b74b52cf054704cb071e57aca4ed2ae Mon Sep 17 00:00:00 2001
From: Tiago Freitas Pereira <tiagofrepereira@gmail.com>
Date: Thu, 31 Mar 2022 13:29:40 +0200
Subject: [PATCH] Created enrollment and scoring functions that accept arrays
as input
---
bob/learn/em/factor_analysis.py | 89 ++++-
bob/learn/em/test/test_jfa.py | 17 +
bob/learn/em/test/test_jfa_trainer.py | 160 +++++++-
doc/guide.rst | 552 +++++++-------------------
doc/index.rst | 1 -
doc/plot/plot_MAP.py | 58 +++
doc/plot/plot_ML.py | 38 +-
7 files changed, 478 insertions(+), 437 deletions(-)
create mode 100644 doc/plot/plot_MAP.py
diff --git a/bob/learn/em/factor_analysis.py b/bob/learn/em/factor_analysis.py
index 318dbba..275a8af 100644
--- a/bob/learn/em/factor_analysis.py
+++ b/bob/learn/em/factor_analysis.py
@@ -2,6 +2,7 @@
# @author: Tiago de Freitas Pereira
+from ast import Return
import logging
import numpy as np
@@ -1105,6 +1106,27 @@ class FactorAnalysisBase(BaseEstimator):
return fn_x.flatten()
+ def score_with_array(self, model, data):
+ """
+ Computes the ISV score using a numpy array as input
+
+ Parameters
+ ----------
+ latent_z : numpy.ndarray
+ Latent representation of the client (E[z_i])
+
+ data : list of :py:class:`bob.learn.em.GMMStats`
+ List of statistics to be scored
+
+ Returns
+ -------
+ score : float
+ The linear scored
+
+ """
+
+ return self.score(model, self.ubm.acc_statistics(data))
+
class ISVMachine(FactorAnalysisBase):
"""
@@ -1210,11 +1232,11 @@ class ISVMachine(FactorAnalysisBase):
y = y.tolist() if not isinstance(y, list) else y
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
n_acc, f_acc = self.initialize(X, y)
for i in range(self.em_iterations):
logger.info("U Training: Iteration %d", i)
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
acc_U_A1, acc_U_A2 = self.e_step(X, y, n_acc, f_acc)
self.m_step(acc_U_A1, acc_U_A2)
@@ -1223,6 +1245,8 @@ class ISVMachine(FactorAnalysisBase):
def enroll(self, X, iterations=1):
"""
Enrolls a new client
+ In ISV, the enrolment is defined as: :math:`m + Dz` with the latent variables `z`
+ representing the enrolled model.
Parameters
----------
@@ -1255,6 +1279,26 @@ class ISVMachine(FactorAnalysisBase):
return latent_z
+ def enroll_with_array(self, X, iterations=1):
+ """
+ Enrolls a new client using a numpy array as input
+
+ Parameters
+ ----------
+ X : array
+ features to be enrolled
+
+ iterations : int
+ Number of iterations to perform
+
+ Returns
+ -------
+ self : object
+ z
+
+ """
+ return self.enroll([self.ubm.acc_statistics(X)], iterations)
+
def score(self, latent_z, data):
"""
Computes the ISV score
@@ -1621,7 +1665,9 @@ class JFAMachine(FactorAnalysisBase):
def enroll(self, X, iterations=1):
"""
- Enrolls a new client
+ Enrolls a new client.
+ In JFA the enrolment is defined as: :math:`m + Vy + Dz` with the latent variables `y` and `z`
+ representing the enrolled model.
Parameters
----------
@@ -1633,8 +1679,8 @@ class JFAMachine(FactorAnalysisBase):
Returns
-------
- self : object
- z, y
+ self : array
+ z, y latent variables
"""
# We have only one class for enrollment
@@ -1656,7 +1702,28 @@ class JFAMachine(FactorAnalysisBase):
X, y, latent_x, latent_y, latent_z, n_acc, f_acc
)
- return latent_y, latent_z
+ # The latent variables are wrapped in to 2axis arrays
+ return latent_y[0], latent_z[0]
+
+ def enroll_with_array(self, X, iterations=1):
+ """
+ Enrolls a new client using a numpy array as input
+
+ Parameters
+ ----------
+ X : array
+ features to be enrolled
+
+ iterations : int
+ Number of iterations to perform
+
+ Returns
+ -------
+ self : object
+ z
+
+ """
+ return self.enroll([self.ubm.acc_statistics(X)], iterations)
def fit(self, X, y):
"""
@@ -1686,13 +1753,13 @@ class JFAMachine(FactorAnalysisBase):
y = y.tolist() if not isinstance(y, list) else y
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
n_acc, f_acc = self.initialize(X, y)
# Updating V
for i in range(self.em_iterations):
logger.info("V Training: Iteration %d", i)
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
acc_V_A1, acc_V_A2 = self.e_step_v(X, y, n_acc, f_acc)
self.m_step_v(acc_V_A1, acc_V_A2)
latent_y = self.finalize_v(X, y, n_acc, f_acc)
@@ -1700,7 +1767,7 @@ class JFAMachine(FactorAnalysisBase):
# Updating U
for i in range(self.em_iterations):
logger.info("U Training: Iteration %d", i)
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
acc_U_A1, acc_U_A2 = self.e_step_u(X, y, latent_y)
self.m_step_u(acc_U_A1, acc_U_A2)
@@ -1709,7 +1776,7 @@ class JFAMachine(FactorAnalysisBase):
# Updating D
for i in range(self.em_iterations):
logger.info("D Training: Iteration %d", i)
- # TODO: Point of parallelism
+ # TODO: Point of MAP-REDUCE
acc_D_A1, acc_D_A2 = self.e_step_d(
X, y, latent_x, latent_y, n_acc, f_acc
)
@@ -1719,7 +1786,7 @@ class JFAMachine(FactorAnalysisBase):
def score(self, model, data):
"""
- Computes the ISV score
+ Computes the JFA score
Parameters
----------
diff --git a/bob/learn/em/test/test_jfa.py b/bob/learn/em/test/test_jfa.py
index c96f59e..de4f761 100644
--- a/bob/learn/em/test/test_jfa.py
+++ b/bob/learn/em/test/test_jfa.py
@@ -55,6 +55,14 @@ def test_JFAMachine():
score = m.score(model, gs)
assert abs(score_ref - score) < eps
+ # Scoring with numpy array
+ np.random.seed(0)
+ X = np.random.normal(loc=0.0, scale=1.0, size=(50, 3))
+ score_ref = 2.028009315286946
+ score = m.score_with_array(model, X)
+
+ assert abs(score_ref - score) < eps
+
def test_ISVMachine():
@@ -97,3 +105,12 @@ def test_ISVMachine():
score_ref = -3.280498193082100
assert abs(score_ref - score) < eps
+
+ # Scoring with numpy array
+ np.random.seed(0)
+ X = np.random.normal(loc=0.0, scale=1.0, size=(50, 3))
+ score_ref = -1.2343813195374242
+
+ score = isv_machine.score_with_array(latent_z, X)
+
+ assert abs(score_ref - score) < eps
diff --git a/bob/learn/em/test/test_jfa_trainer.py b/bob/learn/em/test/test_jfa_trainer.py
index b4b75b7..5d41c7c 100644
--- a/bob/learn/em/test/test_jfa_trainer.py
+++ b/bob/learn/em/test/test_jfa_trainer.py
@@ -213,6 +213,84 @@ def test_JFATrainAndEnrol():
assert np.allclose(latent_z, z_ref, eps)
+def test_JFATrainAndEnrolWithNumpy():
+ # Train and enroll a JFAMachine
+
+ # Calls the train function
+ ubm = GMMMachine(2, 3)
+ ubm.means = UBM_MEAN.reshape((2, 3))
+ ubm.variances = UBM_VAR.reshape((2, 3))
+ it = JFAMachine(ubm, 2, 2, em_iterations=10)
+
+ it.U = copy.deepcopy(M_u)
+ it.V = copy.deepcopy(M_v)
+ it.D = copy.deepcopy(M_d)
+ it.fit(TRAINING_STATS_X, TRAINING_STATS_y)
+
+ v_ref = np.array(
+ [
+ [0.245364911936476, 0.978133261775424],
+ [0.769646805052223, 0.940070736856596],
+ [0.310779202800089, 1.456332053893072],
+ [0.184760934399551, 2.265139705602147],
+ [0.701987784039800, 0.081632150899400],
+ [0.074344030229297, 1.090248340917255],
+ ],
+ "float64",
+ )
+ u_ref = np.array(
+ [
+ [0.049424652628448, 0.060480486336896],
+ [0.178104127464007, 1.884873813495153],
+ [1.204011484266777, 2.281351307871720],
+ [7.278512126426286, -0.390966087173334],
+ [-0.084424326581145, -0.081725474934414],
+ [4.042143689831097, -0.262576386580701],
+ ],
+ "float64",
+ )
+ d_ref = np.array(
+ [
+ 9.648467e-18,
+ 2.63720683155e-12,
+ 2.11822157653706e-10,
+ 9.1047243e-17,
+ 1.41163442535567e-10,
+ 3.30581e-19,
+ ],
+ "float64",
+ )
+
+ eps = 1e-10
+ assert np.allclose(it.V, v_ref, eps)
+ assert np.allclose(it.U, u_ref, eps)
+ assert np.allclose(it.D, d_ref, eps)
+
+ """
+ Calls the enroll function with arrays as input
+ """
+
+ np.random.seed(0)
+ X = np.random.normal(ubm.means[0], scale=0.5, size=(50, 3))
+ latent_y_ref = np.array([-0.13922039, 0.10686916])
+ latent_z_ref = np.array(
+ [
+ [
+ -1.37073043e-17,
+ 1.15641870e-12,
+ -8.29922598e-10,
+ -4.17108194e-16,
+ -2.27107305e-09,
+ 2.94293314e-18,
+ ]
+ ]
+ )
+
+ latent_y, latent_z = it.enroll_with_array(X)
+ assert np.allclose(latent_z, latent_z_ref, eps)
+ assert np.allclose(latent_y, latent_y_ref, eps)
+
+
def test_ISVTrainAndEnrol():
# Train and enroll an 'ISVMachine'
@@ -301,8 +379,86 @@ def test_ISVTrainAndEnrol():
gse = [gse1, gse2]
- latent_z = it.enroll(gse, 5)
- assert np.allclose(latent_z, z_ref, eps)
+
+def test_ISVTrainAndEnrolWithNumpy():
+ # Train and enroll an 'ISVMachine'
+
+ eps = 1e-10
+ d_ref = np.array(
+ [
+ 0.39601136,
+ 0.07348469,
+ 0.47712682,
+ 0.44738127,
+ 0.43179856,
+ 0.45086029,
+ ],
+ "float64",
+ )
+ u_ref = np.array(
+ [
+ [0.855125642430777, 0.563104284748032],
+ [-0.325497865404680, 1.923598985291687],
+ [0.511575659503837, 1.964288663083095],
+ [9.330165761678115, 1.073623827995043],
+ [0.511099245664012, 0.278551249248978],
+ [5.065578541930268, 0.509565618051587],
+ ],
+ "float64",
+ )
+ z_ref = np.array(
+ [
+ -0.079315777443826,
+ 0.092702428248543,
+ -0.342488761656616,
+ -0.059922635809136,
+ 0.133539981073604,
+ 0.213118695516570,
+ ],
+ "float64",
+ )
+
+ """
+ Calls the train function
+ """
+ ubm = GMMMachine(n_gaussians=2)
+ ubm.means = UBM_MEAN.reshape((2, 3))
+ ubm.variances = UBM_VAR.reshape((2, 3))
+
+ it = ISVMachine(
+ ubm,
+ r_U=2,
+ relevance_factor=4.0,
+ em_iterations=10,
+ )
+
+ it.U = copy.deepcopy(M_u)
+ it = it.fit(TRAINING_STATS_X, TRAINING_STATS_y)
+
+ assert np.allclose(it.D, d_ref, eps)
+ assert np.allclose(it.U, u_ref, eps)
+
+ """
+ Calls the enroll function with arrays as input
+ """
+
+ np.random.seed(0)
+ X = np.random.normal(ubm.means[0], scale=0.5, size=(50, 3))
+ latent_z_ref = np.array(
+ [
+ [
+ 0.01084525,
+ 0.06039035,
+ -0.16920933,
+ -0.17321376,
+ -0.9648409,
+ 0.44581105,
+ ]
+ ]
+ )
+
+ latent_z = it.enroll_with_array(X)
+ assert np.allclose(latent_z, latent_z_ref, eps)
def test_JFATrainInitialize():
diff --git a/doc/guide.rst b/doc/guide.rst
index 82d0b95..51e308d 100644
--- a/doc/guide.rst
+++ b/doc/guide.rst
@@ -101,8 +101,8 @@ This statistical model is defined in the class
:options: +NORMALIZE_WHITESPACE +SKIP
>>> import bob.learn.em
- >>> # Create a GMM with k=2 Gaussians with the dimensionality of 3
- >>> gmm_machine = bob.learn.em.GMMMachine(2, 3)
+ >>> # Create a GMM with k=2 Gaussians
+ >>> gmm_machine = bob.learn.em.GMMMachine(n_gaussians=2)
There are plenty of ways to estimate :math:`\Theta`; the next subsections
@@ -118,7 +118,7 @@ the parameters of a statistical model given observations by finding the
:math:`\Theta` that maximizes :math:`P(x|\Theta)` for all :math:`x` in your
dataset [9]_. This optimization is done by the **Expectation-Maximization**
(EM) algorithm [8]_ and it is implemented by
-:py:class:`bob.learn.em.ML_GMMTrainer`.
+:py:class:`bob.learn.em.GMMMachine` by setting the keyword argument `trainer="ml"`.
A very nice explanation of EM algorithm for the maximum likelihood estimation
can be found in this
@@ -130,7 +130,7 @@ estimator.
.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
+ :options: +NORMALIZE_WHITESPACE
>>> import bob.learn.em
>>> import numpy
@@ -141,35 +141,22 @@ estimator.
... [-7,7,-100],
... [-5,5,-101]], dtype='float64')
>>> # Create a kmeans model (machine) m with k=2 clusters
- >>> # with a dimensionality equal to 3
- >>> gmm_machine = bob.learn.em.GMMMachine(2, 3)
- >>> # Using the MLE trainer to train the GMM:
- >>> # True, True, True means update means/variances/weights at each
- >>> # iteration
- >>> gmm_trainer = bob.learn.em.ML_GMMTrainer(True, True, True)
- >>> # Setting some means to start the training.
- >>> # In practice, the output of kmeans is a good start for the MLE training
- >>> gmm_machine.means = numpy.array(
- ... [[ -4., 2.3, -10.5],
- ... [ 2.5, -4.5, 59. ]])
- >>> max_iterations = 200
- >>> convergence_threshold = 1e-5
+ >>> # and using the MLE trainer to train the GMM:
+ >>> # In this setup, kmeans is used to initialize the means, variances and weights of the gaussians
+ >>> gmm_machine = bob.learn.em.GMMMachine(n_gaussians=2, trainer="ml")
>>> # Training
- >>> bob.learn.em.train(gmm_trainer, gmm_machine, data,
- ... max_iterations=max_iterations,
- ... convergence_threshold=convergence_threshold)
+ >>> gmm_machine = gmm_machine.fit(data)
>>> print(gmm_machine.means)
- [[ -6. 6. -100.5]
- [ 3.5 -3.5 99. ]]
+ [[ 3.5 -3.5 99. ]
+ [ -6. 6. -100.5]]
Bellow follow an intuition of the GMM trained the maximum likelihood estimator
using the Iris flower
`dataset <https://en.wikipedia.org/wiki/Iris_flower_data_set>`_.
-..
- TODO uncomment when implemented
- .. plot:: plot/plot_ML.py
- :include-source: False
+
+.. plot:: plot/plot_ML.py
+ :include-source: False
Maximum a posteriori Estimator (MAP)
@@ -181,7 +168,7 @@ estimate that equals the mode of the posterior distribution by incorporating in
its loss function a prior distribution [10]_. Commonly this prior distribution
(the values of :math:`\Theta`) is estimated with MLE. This optimization is done
by the **Expectation-Maximization** (EM) algorithm [8]_ and it is implemented
-by :py:class:`bob.learn.em.MAP_GMMTrainer`.
+by :py:class:`bob.learn.em.GMMMachine` by setting the keyword argument `trainer="map"`.
A compact way to write relevance MAP adaptation is by using GMM supervector
notation (this will be useful in the next subsections). The GMM supervector
@@ -195,7 +182,7 @@ Follow bellow an snippet on how to train a GMM using the MAP estimator.
.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
+ :options: +NORMALIZE_WHITESPACE
>>> import bob.learn.em
>>> import numpy
@@ -206,33 +193,31 @@ Follow bellow an snippet on how to train a GMM using the MAP estimator.
... [-7,7,-100],
... [-5,5,-101]], dtype='float64')
>>> # Creating a fake prior
- >>> prior_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> # Set some random means for the example
+ >>> prior_gmm = bob.learn.em.GMMMachine(2)
+ >>> # Set some random means/variances and weights for the example
>>> prior_gmm.means = numpy.array(
... [[ -4., 2.3, -10.5],
... [ 2.5, -4.5, 59. ]])
- >>> # Creating the model for the adapted GMM
- >>> adapted_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> # Creating the MAP trainer
- >>> gmm_trainer = bob.learn.em.MAP_GMMTrainer(prior_gmm, relevance_factor=4)
- >>>
- >>> max_iterations = 200
- >>> convergence_threshold = 1e-5
+ >>> prior_gmm.variances = numpy.array(
+ ... [[ -0.1, 0.5, -0.5],
+ ... [ 0.5, -0.5, 0.2 ]])
+ >>> prior_gmm.weights = numpy.array([ 0.8, 0.5])
+ >>> # Creating the model for the adapted GMM, and setting the `prior_gmm` as the source GMM
+ >>> # note that we have set `trainer="map"`, so we use the Maximum a posteriori estimator
+ >>> adapted_gmm = bob.learn.em.GMMMachine(2, ubm=prior_gmm, trainer="map")
>>> # Training
- >>> bob.learn.em.train(gmm_trainer, adapted_gmm, data,
- ... max_iterations=max_iterations,
- ... convergence_threshold=convergence_threshold)
+ >>> adapted_gmm = adapted_gmm.fit(data)
>>> print(adapted_gmm.means)
- [[ -4.667 3.533 -40.5 ]
- [ 2.929 -4.071 76.143]]
+ [[ -4. 2.3 -10.5 ]
+ [ 0.944 -1.833 36.889]]
Bellow follow an intuition of the GMM trained with the MAP estimator using the
Iris flower `dataset <https://en.wikipedia.org/wiki/Iris_flower_data_set>`_.
+It can be observed how the MAP means (the red triangles) around the center of each class
+from a prior GMM (the blue crosses).
-..
- TODO uncomment when implemented
- .. plot:: plot/plot_MAP.py
- :include-source: False
+.. plot:: plot/plot_MAP.py
+ :include-source: False
Session Variability Modeling with Gaussian Mixture Models
@@ -273,7 +258,7 @@ prior GMM.
.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
+ :options: +NORMALIZE_WHITESPACE
>>> import bob.learn.em
>>> import numpy
@@ -285,21 +270,13 @@ prior GMM.
... [-0.3, -0.1, 0],
... [1.2, 1.4, 1],
... [0.8, 1., 1]], dtype='float64')
- >>> # Creating a fake prior with 2 Gaussians of dimension 3
- >>> prior_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> prior_gmm.means = numpy.vstack((numpy.random.normal(0, 0.5, (1, 3)),
- ... numpy.random.normal(1, 0.5, (1, 3))))
- >>> # All nice and round diagonal covariance
- >>> prior_gmm.variances = numpy.ones((2, 3)) * 0.5
- >>> prior_gmm.weights = numpy.array([0.3, 0.7])
+ >>> # Training a GMM with 2 Gaussians of dimension 3
+ >>> prior_gmm = bob.learn.em.GMMMachine(2).fit(data)
>>> # Creating the container
- >>> gmm_stats_container = bob.learn.em.GMMStats(2, 3)
- >>> for d in data:
- ... prior_gmm.acc_statistics(d, gmm_stats_container)
- >>>
+ >>> gmm_stats = prior_gmm.acc_statistics(data)
>>> # Printing the responsibilities
- >>> print(gmm_stats_container.n/gmm_stats_container.t)
- [0.429 0.571]
+ >>> print(gmm_stats.n/gmm_stats.t)
+ [0.6 0.4]
Inter-Session Variability
@@ -307,80 +284,81 @@ Inter-Session Variability
.. _isv:
Inter-Session Variability (ISV) modeling [3]_ [2]_ is a session variability
-modeling technique built on top of the Gaussian mixture modeling approach. It
-hypothesizes that within-class variations are embedded in a linear subspace in
-the GMM means subspace and these variations can be suppressed by an offset w.r.t
-each mean during the MAP adaptation.
+modeling technique built on top of the Gaussian mixture modeling approach.
+It hypothesizes that within-class variations are embedded in a linear subspace in
+the GMM means subspace, and these variations can be suppressed by an offset w.r.t each mean during the MAP adaptation.
-In this generative model each sample is assumed to have been generated by a GMM
-mean supervector with the following shape:
+
+In this generative model, each sample is assumed to have been generated by a GMM mean supervector with the following shape:
:math:`\mu_{i, j} = m + Ux_{i, j} + D_z{i}`, where :math:`m` is our prior,
:math:`Ux_{i, j}` is the session offset that we want to suppress and
:math:`D_z{i}` is the class offset (with all session effects suppressed).
-All possible sources of session variations is embedded in this matrix
-:math:`U`. Follow bellow an intuition of what is modeled with :math:`U` in the
+It is hypothesized that all possible sources of session variations are embedded in this matrix
+:math:`U`. Follow below an intuition of what is modeled with :math:`U` in the
Iris flower `dataset <https://en.wikipedia.org/wiki/Iris_flower_data_set>`_.
The arrows :math:`U_{1}`, :math:`U_{2}` and :math:`U_{3}` are the directions of
-the within class variations, with respect to each Gaussian component, that will
+the within-class variations, with respect to each Gaussian component, that will
be suppressed a posteriori.
-..
- TODO uncomment when implemented
- .. plot:: plot/plot_ISV.py
- :include-source: False
+
+
+.. plot:: plot/plot_ISV.py
+ :include-source: False
The ISV statistical model is stored in this container
-:py:class:`bob.learn.em.ISVBase` and the training is performed by
-:py:class:`bob.learn.em.ISVTrainer`. The snippet bellow shows how to train a
-Intersession variability modeling.
+:py:class:`bob.learn.em.ISVMachine`.
+The snippet bellow shows how to:
+
+ - Train a Intersession variability modeling.
+ - Enroll a subject with such a model.
+ - Compute score with such a model.
.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
+ :options: +NORMALIZE_WHITESPACE
+
+ >>> import bob.learn.em
+ >>> import numpy as np
+
+ >>> np.random.seed(10)
+
+ >>> # Generating some fake data
+ >>> data_class1 = np.random.normal(0, 0.5, (10, 3))
+ >>> data_class2 = np.random.normal(-0.2, 0.2, (10, 3))
+ >>> X = np.vstack((data_class1, data_class2))
+ >>> y = np.hstack((np.zeros(10, dtype=int), np.ones(10, dtype=int)))
+ >>> # Training an UBM with 2 gaussians
+ >>> ubm = bob.learn.em.GMMMachine(2).fit(X)
+
+ >>> # The input the the ISV Training is the statistics of the GMM
+ >>> # Here we are creating a GMMStats for each datapoints, which is NOT usual,
+ >>> # but it is done for testing purposes
+ >>> gmm_stats = [ubm.acc_statistics(x[np.newaxis]) for x in X]
+
+ >>> # Finally doing the ISV training with U subspace with dimension of 2
+ >>> isv_machine = bob.learn.em.ISVMachine(ubm, r_U=2).fit(gmm_stats, y)
+ >>> print(isv_machine.U)
+ [[-0.079 -0.011]
+ [ 0.078 0.039]
+ [ 0.129 0.018]
+ [ 0.175 0.254]
+ [ 0.019 0.027]
+ [-0.132 -0.191]]
+
+ >>> # Enrolling a subject
+ >>> enroll_data = np.array([[1.2, 0.1, 1.4], [0.5, 0.2, 0.3]])
+ >>> model = isv_machine.enroll_with_array(enroll_data)
+ >>> print(model)
+ [[ 0.54 0.246 0.505 1.617 -0.791 0.746]]
+
+ >>> # Probing
+ >>> probe_data = np.array([[1.2, 0.1, 1.4], [0.5, 0.2, 0.3]])
+ >>> score = isv_machine.score_with_array(model, probe_data)
+ >>> print(score)
+ [2.754]
- >>> import bob.learn.em
- >>> import numpy
- >>> numpy.random.seed(10)
- >>>
- >>> # Generating some fake data
- >>> data_class1 = numpy.random.normal(0, 0.5, (10, 3))
- >>> data_class2 = numpy.random.normal(-0.2, 0.2, (10, 3))
- >>> data = [data_class1, data_class2]
-
- >>> # Creating a fake prior with 2 gaussians of dimension 3
- >>> prior_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> prior_gmm.means = numpy.vstack((numpy.random.normal(0, 0.5, (1, 3)),
- ... numpy.random.normal(1, 0.5, (1, 3))))
- >>> # All nice and round diagonal covariance
- >>> prior_gmm.variances = numpy.ones((2, 3)) * 0.5
- >>> prior_gmm.weights = numpy.array([0.3, 0.7])
- >>> # The input the the ISV Training is the statistics of the GMM
- >>> gmm_stats_per_class = []
- >>> for d in data:
- ... stats = []
- ... for i in d:
- ... gmm_stats_container = bob.learn.em.GMMStats(2, 3)
- ... prior_gmm.acc_statistics(i, gmm_stats_container)
- ... stats.append(gmm_stats_container)
- ... gmm_stats_per_class.append(stats)
-
- >>> # Finally doing the ISV training
- >>> subspace_dimension_of_u = 2
- >>> relevance_factor = 4
- >>> isvbase = bob.learn.em.ISVBase(prior_gmm, subspace_dimension_of_u)
- >>> trainer = bob.learn.em.ISVTrainer(relevance_factor)
- >>> bob.learn.em.train(trainer, isvbase, gmm_stats_per_class,
- ... max_iterations=50)
- >>> # Printing the session offset w.r.t each Gaussian component
- >>> print(isvbase.u)
- [[-0.01 -0.027]
- [-0.002 -0.004]
- [ 0.028 0.074]
- [ 0.012 0.03 ]
- [ 0.033 0.085]
- [ 0.046 0.12 ]]
Joint Factor Analysis
@@ -401,308 +379,59 @@ between class variations with respect to each Gaussian component that will be
added a posteriori.
-..
- TODO uncomment when implemented
- .. plot:: plot/plot_JFA.py
- :include-source: False
+.. plot:: plot/plot_JFA.py
+ :include-source: False
The JFA statistical model is stored in this container
-:py:class:`bob.learn.em.JFABase` and the training is performed by
-:py:class:`bob.learn.em.JFATrainer`. The snippet bellow shows how to train a
-Intersession variability modeling.
-
-.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
-
- >>> import bob.learn.em
- >>> import numpy
- >>> numpy.random.seed(10)
- >>>
- >>> # Generating some fake data
- >>> data_class1 = numpy.random.normal(0, 0.5, (10, 3))
- >>> data_class2 = numpy.random.normal(-0.2, 0.2, (10, 3))
- >>> data = [data_class1, data_class2]
-
- >>> # Creating a fake prior with 2 Gaussians of dimension 3
- >>> prior_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> prior_gmm.means = numpy.vstack((numpy.random.normal(0, 0.5, (1, 3)),
- ... numpy.random.normal(1, 0.5, (1, 3))))
- >>> # All nice and round diagonal covariance
- >>> prior_gmm.variances = numpy.ones((2, 3)) * 0.5
- >>> prior_gmm.weights = numpy.array([0.3, 0.7])
- >>>
- >>> # The input the the JFA Training is the statistics of the GMM
- >>> gmm_stats_per_class = []
- >>> for d in data:
- ... stats = []
- ... for i in d:
- ... gmm_stats_container = bob.learn.em.GMMStats(2, 3)
- ... prior_gmm.acc_statistics(i, gmm_stats_container)
- ... stats.append(gmm_stats_container)
- ... gmm_stats_per_class.append(stats)
- >>>
- >>> # Finally doing the JFA training
- >>> subspace_dimension_of_u = 2
- >>> subspace_dimension_of_v = 2
- >>> relevance_factor = 4
- >>> jfabase = bob.learn.em.JFABase(prior_gmm, subspace_dimension_of_u,
- ... subspace_dimension_of_v)
- >>> trainer = bob.learn.em.JFATrainer()
- >>> bob.learn.em.train_jfa(trainer, jfabase, gmm_stats_per_class,
- ... max_iterations=50)
-
- >>> # Printing the session offset w.r.t each Gaussian component
- >>> print(jfabase.v)
- [[ 0.003 -0.006]
- [ 0.041 -0.084]
- [-0.261 0.53 ]
- [-0.252 0.51 ]
- [-0.387 0.785]
- [-0.36 0.73 ]]
-
-Total variability Modelling
-===========================
-.. _ivector:
-
-Total Variability (TV) modeling [4]_ is a front-end initially introduced for
-speaker recognition, which aims at describing samples by vectors of low
-dimensionality called ``i-vectors``. The model consists of a subspace :math:`T`
-and a residual diagonal covariance matrix :math:`\Sigma`, that are then used to
-extract i-vectors, and is built upon the GMM approach. In the supervector
-notation this modeling has the following shape: :math:`\mu = m + Tv`.
-
-Follow bellow an intuition of the data from the Iris flower
-`dataset <https://en.wikipedia.org/wiki/Iris_flower_data_set>`_, embedded in
-the iVector space.
-
-..
- TODO uncomment when implemented
- .. plot:: plot/plot_iVector.py
- :include-source: False
-
-
-The iVector statistical model is stored in this container
-:py:class:`bob.learn.em.IVectorMachine` and the training is performed by
-:py:class:`bob.learn.em.IVectorTrainer`. The snippet bellow shows how to train
-a Total variability modeling.
-
-.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
-
- >>> import bob.learn.em
- >>> import numpy
- >>> numpy.random.seed(10)
- >>>
- >>> # Generating some fake data
- >>> data_class1 = numpy.random.normal(0, 0.5, (10, 3))
- >>> data_class2 = numpy.random.normal(-0.2, 0.2, (10, 3))
- >>> data = [data_class1, data_class2]
- >>>
- >>> # Creating a fake prior with 2 gaussians of dimension 3
- >>> prior_gmm = bob.learn.em.GMMMachine(2, 3)
- >>> prior_gmm.means = numpy.vstack((numpy.random.normal(0, 0.5, (1, 3)),
- ... numpy.random.normal(1, 0.5, (1, 3))))
- >>> # All nice and round diagonal covariance
- >>> prior_gmm.variances = numpy.ones((2, 3)) * 0.5
- >>> prior_gmm.weights = numpy.array([0.3, 0.7])
- >>>
- >>> # The input the the TV Training is the statistics of the GMM
- >>> gmm_stats_per_class = []
- >>> for d in data:
- ... for i in d:
- ... gmm_stats_container = bob.learn.em.GMMStats(2, 3)
- ... prior_gmm.acc_statistics(i, gmm_stats_container)
- ... gmm_stats_per_class.append(gmm_stats_container)
- >>>
- >>> # Finally doing the TV training
- >>> subspace_dimension_of_t = 2
- >>>
- >>> ivector_trainer = bob.learn.em.IVectorTrainer(update_sigma=True)
- >>> ivector_machine = bob.learn.em.IVectorMachine(
- ... prior_gmm, subspace_dimension_of_t, 10e-5)
- >>> # train IVector model
- >>> bob.learn.em.train(ivector_trainer, ivector_machine,
- ... gmm_stats_per_class, 500)
- >>>
- >>> # Printing the session offset w.r.t each Gaussian component
- >>> print(ivector_machine.t)
- [[ 0.11 -0.203]
- [-0.124 0.014]
- [ 0.296 0.674]
- [ 0.447 0.174]
- [ 0.425 0.583]
- [ 0.394 0.794]]
-
-Linear Scoring
-==============
-.. _linearscoring:
-
-In :ref:`MAP <map>` adaptation, :ref:`ISV <isv>` and :ref:`JFA <jfa>` a
-traditional way to do scoring is via the log-likelihood ratio between the
-adapted model and the prior as the following:
-
-.. math::
- score = ln(P(x | \Theta)) - ln(P(x | \Theta_{prior})),
+:py:class:`bob.learn.em.JFAMachine`. The snippet bellow shows how to train a
+such session variability model.
+ - Train a JFA model.
+ - Enroll a subject with such a model.
+ - Compute score with such a model.
-(with :math:`\Theta` varying for each approach).
-
-A simplification proposed by [Glembek2009]_, called linear scoring,
-approximate this ratio using a first order Taylor series as the following:
-
-.. math::
- score = \frac{\mu - \mu_{prior}}{\sigma_{prior}} f * (\mu_{prior} + U_x),
-
-where :math:`\mu` is the the GMM mean supervector (of the prior and the adapted
-model), :math:`\sigma` is the variance, supervector, :math:`f` is the first
-order GMM statistics (:py:class:`bob.learn.em.GMMStats.sum_px`) and
-:math:`U_x`, is possible channel offset (:ref:`ISV <isv>`).
-
-This scoring technique is implemented in :py:func:`bob.learn.em.linear_scoring`.
-The snippet bellow shows how to compute scores using this approximation.
.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
+ :options: +NORMALIZE_WHITESPACE
>>> import bob.learn.em
- >>> import numpy
- >>> # Defining a fake prior
- >>> prior_gmm = bob.learn.em.GMMMachine(3, 2)
- >>> prior_gmm.means = numpy.array([[1, 1], [2, 2.1], [3, 3]])
- >>> # Defining a fake prior
- >>> adapted_gmm = bob.learn.em.GMMMachine(3,2)
- >>> adapted_gmm.means = numpy.array([[1.5, 1.5], [2.5, 2.5], [2, 2]])
- >>> # Defining an input
- >>> input = numpy.array([[1.5, 1.5], [1.6, 1.6]])
- >>> #Accumulating statistics of the GMM
- >>> stats = bob.learn.em.GMMStats(3, 2)
- >>> prior_gmm.acc_statistics(input, stats)
- >>> score = bob.learn.em.linear_scoring(
- ... [adapted_gmm], prior_gmm, [stats], [],
- ... frame_length_normalisation=True)
+ >>> import numpy as np
+
+ >>> np.random.seed(10)
+
+ >>> # Generating some fake data
+ >>> data_class1 = np.random.normal(0, 0.5, (10, 3))
+ >>> data_class2 = np.random.normal(-0.2, 0.2, (10, 3))
+ >>> X = np.vstack((data_class1, data_class2))
+ >>> y = np.hstack((np.zeros(10, dtype=int), np.ones(10, dtype=int)))
+ >>> # Training an UBM with 2 gaussians
+ >>> ubm = bob.learn.em.GMMMachine(2).fit(X)
+
+ >>> # The input the the JFA Training is the statistics of the GMM
+ >>> # Here we are creating a GMMStats for each datapoints, which is NOT usual,
+ >>> # but it is done for testing purposes
+ >>> gmm_stats = [ubm.acc_statistics(x[np.newaxis]) for x in X]
+
+ >>> # Finally doing the JFA training with U and V subspaces with dimension of 2
+ >>> jfa_machine = bob.learn.em.JFAMachine(ubm, r_U=2, r_V=2).fit(gmm_stats, y)
+ >>> print(jfa_machine.U)
+ [[-0.069 -0.029]
+ [ 0.079 0.039]
+ [ 0.123 0.042]
+ [ 0.17 0.255]
+ [ 0.018 0.027]
+ [-0.128 -0.192]]
+
+ >>> enroll_data = np.array([[1.2, 0.1, 1.4], [0.5, 0.2, 0.3]])
+ >>> model = jfa_machine.enroll_with_array(enroll_data)
+ >>> print(model)
+ (array([0.634, 0.165]), array([ 0., 0., 0., 0., -0., 0.]))
+
+ >>> probe_data = np.array([[1.2, 0.1, 1.4], [0.5, 0.2, 0.3]])
+ >>> score = jfa_machine.score_with_array(model, probe_data)
>>> print(score)
- [[0.254]]
-
-
-Probabilistic Linear Discriminant Analysis (PLDA)
--------------------------------------------------
-
-Probabilistic Linear Discriminant Analysis [5]_ is a probabilistic model that
-incorporates components describing both between-class and within-class
-variations. Given a mean :math:`\mu`, between-class and within-class subspaces
-:math:`F` and :math:`G` and residual noise :math:`\epsilon` with zero mean and
-diagonal covariance matrix :math:`\Sigma`, the model assumes that a sample
-:math:`x_{i,j}` is generated by the following process:
-
-.. math::
-
- x_{i,j} = \mu + F h_{i} + G w_{i,j} + \epsilon_{i,j}
-
-
-An Expectation-Maximization algorithm can be used to learn the parameters of
-this model :math:`\mu`, :math:`F` :math:`G` and :math:`\Sigma`. As these
-parameters can be shared between classes, there is a specific container class
-for this purpose, which is :py:class:`bob.learn.em.PLDABase`. The process is
-described in detail in [6]_.
-
-Let us consider a training set of two classes, each with 3 samples of
-dimensionality 3.
-
-.. doctest::
- :options: +NORMALIZE_WHITESPACE +SKIP
-
- >>> data1 = numpy.array(
- ... [[3,-3,100],
- ... [4,-4,50],
- ... [40,-40,150]], dtype=numpy.float64)
- >>> data2 = numpy.array(
- ... [[3,6,-50],
- ... [4,8,-100],
- ... [40,79,-800]], dtype=numpy.float64)
- >>> data = [data1,data2]
-
-Learning a PLDA model can be performed by instantiating the class
-:py:class:`bob.learn.em.PLDATrainer`, and calling the
-:py:meth:`bob.learn.em.train` method.
-
-.. doctest::
- :options: +SKIP
-
- >>> # This creates a PLDABase container for input feature of dimensionality
- >>> # 3 and with subspaces F and G of rank 1 and 2, respectively.
- >>> pldabase = bob.learn.em.PLDABase(3,1,2)
-
- >>> trainer = bob.learn.em.PLDATrainer()
- >>> bob.learn.em.train(trainer, pldabase, data, max_iterations=10)
-
-Once trained, this PLDA model can be used to compute the log-likelihood of a
-set of samples given some hypothesis. For this purpose, a
-:py:class:`bob.learn.em.PLDAMachine` should be instantiated. Then, the
-log-likelihood that a set of samples share the same latent identity variable
-:math:`h_{i}` (i.e. the samples are coming from the same identity/class) is
-obtained by calling the
-:py:meth:`bob.learn.em.PLDAMachine.compute_log_likelihood()` method.
-
-.. doctest::
- :options: +SKIP
-
- >>> plda = bob.learn.em.PLDAMachine(pldabase)
- >>> samples = numpy.array(
- ... [[3.5,-3.4,102],
- ... [4.5,-4.3,56]], dtype=numpy.float64)
- >>> loglike = plda.compute_log_likelihood(samples)
-
-If separate models for different classes need to be enrolled, each of them with
-a set of enrollment samples, then, several instances of
-:py:class:`bob.learn.em.PLDAMachine` need to be created and enrolled using
-the :py:meth:`bob.learn.em.PLDATrainer.enroll()` method as follows.
-
-.. doctest::
- :options: +SKIP
-
- >>> plda1 = bob.learn.em.PLDAMachine(pldabase)
- >>> samples1 = numpy.array(
- ... [[3.5,-3.4,102],
- ... [4.5,-4.3,56]], dtype=numpy.float64)
- >>> trainer.enroll(plda1, samples1)
- >>> plda2 = bob.learn.em.PLDAMachine(pldabase)
- >>> samples2 = numpy.array(
- ... [[3.5,7,-49],
- ... [4.5,8.9,-99]], dtype=numpy.float64)
- >>> trainer.enroll(plda2, samples2)
-
-Afterwards, the joint log-likelihood of the enrollment samples and of one or
-several test samples can be computed as previously described, and this
-separately for each model.
-
-.. doctest::
- :options: +SKIP
-
- >>> sample = numpy.array([3.2,-3.3,58], dtype=numpy.float64)
- >>> l1 = plda1.compute_log_likelihood(sample)
- >>> l2 = plda2.compute_log_likelihood(sample)
-
-In a verification scenario, there are two possible hypotheses:
-
-#. :math:`x_{test}` and :math:`x_{enroll}` share the same class.
-#. :math:`x_{test}` and :math:`x_{enroll}` are from different classes.
-
-Using the methods :py:meth:`bob.learn.em.PLDAMachine.log_likelihood_ratio` or
-its alias ``__call__`` function, the corresponding log-likelihood ratio will be
-computed, which is defined in more formal way by:
-:math:`s = \ln(P(x_{test},x_{enroll})) - \ln(P(x_{test})P(x_{enroll}))`
-
-.. doctest::
- :options: +SKIP
-
- >>> s1 = plda1(sample)
- >>> s2 = plda2(sample)
-
-.. testcleanup:: *
+ [0.471]
- import shutil
- os.chdir(current_directory)
- shutil.rmtree(temp_dir)
@@ -711,9 +440,6 @@ computed, which is defined in more formal way by:
.. [1] http://dx.doi.org/10.1109/TASL.2006.881693
.. [2] http://publications.idiap.ch/index.php/publications/show/2606
.. [3] http://dx.doi.org/10.1016/j.csl.2007.05.003
-.. [4] http://dx.doi.org/10.1109/TASL.2010.2064307
-.. [5] http://dx.doi.org/10.1109/ICCV.2007.4409052
-.. [6] http://doi.ieeecomputersociety.org/10.1109/TPAMI.2013.38
.. [7] http://en.wikipedia.org/wiki/K-means_clustering
.. [8] http://en.wikipedia.org/wiki/Expectation-maximization_algorithm
.. [9] http://en.wikipedia.org/wiki/Maximum_likelihood
diff --git a/doc/index.rst b/doc/index.rst
index 14a5f1d..2e35eef 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -51,7 +51,6 @@ References
..
.. [Roweis1998] Roweis, Sam. "EM algorithms for PCA and SPCA." Advances in neural information processing systems (1998): 626-632.
-.. [Glembek2009] Glembek, Ondrej, et al. "Comparison of scoring methods used in speaker recognition with joint factor analysis." Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on. IEEE, 2009.
Indices and tables
diff --git a/doc/plot/plot_MAP.py b/doc/plot/plot_MAP.py
new file mode 100644
index 0000000..f668c8c
--- /dev/null
+++ b/doc/plot/plot_MAP.py
@@ -0,0 +1,58 @@
+import matplotlib.pyplot as plt
+from sklearn.datasets import load_iris
+
+import bob.learn.em
+import numpy as np
+
+np.random.seed(10)
+
+iris_data = load_iris()
+data = np.column_stack((iris_data.data[:, 0], iris_data.data[:, 3]))
+setosa = data[iris_data.target == 0]
+versicolor = data[iris_data.target == 1]
+virginica = data[iris_data.target == 2]
+
+
+# Two clusters with
+mle_machine = bob.learn.em.GMMMachine(3)
+# Creating some fake means for the example
+mle_machine.means = np.array([[5, 3], [4, 2], [7, 3.0]])
+mle_machine.variances = np.array([[0.1, 0.5], [0.2, 0.2], [0.7, 0.5]])
+
+
+# Creating some random data centered in
+map_machine = bob.learn.em.GMMMachine(
+ 3, trainer="map", ubm=mle_machine, map_relevance_factor=4
+).fit(data)
+
+
+figure, ax = plt.subplots()
+# plt.scatter(data[:, 0], data[:, 1], c="olivedrab", label="new data")
+plt.scatter(setosa[:, 0], setosa[:, 1], c="darkcyan", label="setosa")
+plt.scatter(
+ versicolor[:, 0], versicolor[:, 1], c="goldenrod", label="versicolor"
+)
+plt.scatter(virginica[:, 0], virginica[:, 1], c="dimgrey", label="virginica")
+plt.scatter(
+ mle_machine.means[:, 0],
+ mle_machine.means[:, 1],
+ c="blue",
+ marker="x",
+ label="prior centroids - mle",
+ s=60,
+)
+plt.scatter(
+ map_machine.means[:, 0],
+ map_machine.means[:, 1],
+ c="red",
+ marker="^",
+ label="adapted centroids - map",
+ s=60,
+)
+plt.legend()
+plt.xticks([], [])
+plt.yticks([], [])
+ax.set_xlabel("Sepal length")
+ax.set_ylabel("Petal width")
+plt.tight_layout()
+plt.show()
diff --git a/doc/plot/plot_ML.py b/doc/plot/plot_ML.py
index 32f6643..410abf0 100644
--- a/doc/plot/plot_ML.py
+++ b/doc/plot/plot_ML.py
@@ -1,7 +1,7 @@
import logging
import matplotlib.pyplot as plt
-import numpy
+import numpy as np
from matplotlib.lines import Line2D
from matplotlib.patches import Ellipse
@@ -13,7 +13,7 @@ logger = logging.getLogger("bob.learn.em")
logger.setLevel("DEBUG")
iris_data = load_iris()
-data = iris_data.data
+data = np.column_stack((iris_data.data[:, 0], iris_data.data[:, 3]))
setosa = data[iris_data.target == 0]
versicolor = data[iris_data.target == 1]
virginica = data[iris_data.target == 2]
@@ -28,7 +28,6 @@ machine = GMMMachine(
)
# Initialize the means with known values (optional, skips kmeans)
-machine.means = numpy.array([[5, 3], [4, 2], [7, 3]], dtype=float)
machine = machine.fit(data)
@@ -48,14 +47,33 @@ ax.scatter(
s=60,
)
+
+def draw_ellipse(position, covariance, ax=None, **kwargs):
+ """
+ Draw an ellipse with a given position and covariance
+ """
+ ax = ax or plt.gca()
+
+ # Convert covariance to principal axes
+ if covariance.shape == (2, 2):
+ U, s, Vt = np.linalg.svd(covariance)
+ angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
+ width, height = 2 * np.sqrt(s)
+ else:
+ angle = 0
+ width, height = 2 * np.sqrt(covariance)
+
+ # Draw the Ellipse
+ for nsig in range(1, 4):
+ ax.add_patch(
+ Ellipse(position, nsig * width, nsig * height, angle, **kwargs)
+ )
+
+
# Draw ellipses for covariance
-for mean, variance in zip(machine.means, machine.variances):
- eigvals, eigvecs = numpy.linalg.eig(numpy.diag(variance))
- axis = numpy.sqrt(eigvals) * numpy.sqrt(5.991)
- angle = 180.0 * numpy.arctan(eigvecs[1][0] / eigvecs[1][1]) / numpy.pi
- ax.add_patch(
- Ellipse(mean, *axis, angle=angle, linewidth=1, fill=False, zorder=2)
- )
+w_factor = 0.2 / np.max(machine.weights)
+for w, pos, covar in zip(machine.weights, machine.means, machine.variances):
+ draw_ellipse(pos, covar, alpha=w * w_factor)
# Plot details (legend, axis labels)
plt.legend(
--
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