From 9b0757a449e3559599d59690f54cae81576dc23d Mon Sep 17 00:00:00 2001
From: Tiago Freitas Pereira <tiagofrepereira@gmail.com>
Date: Wed, 30 Mar 2022 14:26:36 +0200
Subject: [PATCH] [sphinx] Update the documentation
---
.pre-commit-config.yaml | 5 +
bob/learn/em/__init__.py | 2 +-
bob/learn/em/factor_analysis.py | 92 +++++-----
bob/learn/em/test/test_jfa.py | 3 +-
bob/learn/em/test/test_jfa_trainer.py | 52 ++----
bob/learn/em/wccn.py | 3 +
bob/learn/em/whitening.py | 3 +
buildout.cfg | 1 +
doc/index.rst | 4 +-
doc/plot/plot_ISV.py | 168 ++++++++++++++++++
doc/plot/plot_JFA.py | 240 ++++++++++++++++++++++++++
11 files changed, 486 insertions(+), 87 deletions(-)
create mode 100644 doc/plot/plot_ISV.py
create mode 100644 doc/plot/plot_JFA.py
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 1daa230..833ff23 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -14,6 +14,11 @@ repos:
rev: 3.9.2
hooks:
- id: flake8
+ exclude: |
+ (?x)^(
+ bob/devtools/templates/setup.py|
+ deps/bob-devel/run_test.py
+ )$
- repo: https://github.com/pre-commit/pre-commit-hooks
rev: v4.1.0
hooks:
diff --git a/bob/learn/em/__init__.py b/bob/learn/em/__init__.py
index 669a8a3..fda23d6 100644
--- a/bob/learn/em/__init__.py
+++ b/bob/learn/em/__init__.py
@@ -1,11 +1,11 @@
import bob.extension
+from .factor_analysis import ISVMachine, JFAMachine
from .gmm import GMMMachine, GMMStats
from .kmeans import KMeansMachine
from .linear_scoring import linear_scoring # noqa: F401
from .wccn import WCCN
from .whitening import Whitening
-from .factor_analysis import ISVMachine, JFAMachine
def get_config():
diff --git a/bob/learn/em/factor_analysis.py b/bob/learn/em/factor_analysis.py
index 6eb2cd4..318dbba 100644
--- a/bob/learn/em/factor_analysis.py
+++ b/bob/learn/em/factor_analysis.py
@@ -7,7 +7,8 @@ import logging
import numpy as np
from sklearn.base import BaseEstimator
-from . import linear_scoring
+
+from .linear_scoring import linear_scoring
logger = logging.getLogger(__name__)
@@ -317,7 +318,9 @@ class FactorAnalysisBase(BaseEstimator):
X = np.array(X)
return list(X[np.where(np.array(y) == i)[0]])
- #################### Estimating U and x ######################
+ """
+ Estimating U and x
+ """
def _compute_id_plus_u_prod_ih(self, x_i, UProd):
"""
@@ -340,7 +343,7 @@ class FactorAnalysisBase(BaseEstimator):
"""
n_i = x_i.n
- I = np.eye(self.r_U, self.r_U)
+ I = np.eye(self.r_U, self.r_U) # noqa: E741
# TODO: make the invertion matrix function as a parameter
return np.linalg.inv(I + (UProd * n_i[:, None, None]).sum(axis=0))
@@ -362,13 +365,12 @@ class FactorAnalysisBase(BaseEstimator):
E[y_i] for class `i`
"""
-
f_i = x_i.sum_px
n_i = x_i.n
- n_ic = np.repeat(n_i, self.supervector_dimension // 2)
+ n_ic = np.repeat(n_i, self.feature_dimension)
V = self._V
- ## N_ih*( m + D*z)
+ # N_ih*( m + D*z)
# z is zero when the computation flow comes from update_X
if latent_z_i is None:
# Fn_x_ih = N_{i,h}*(o_{i,h} - m)
@@ -474,7 +476,7 @@ class FactorAnalysisBase(BaseEstimator):
Computes U_c.T*inv(Sigma_c) @ U_c.T
- ### https://gitlab.idiap.ch/bob/bob.learn.em/-/blob/da92d0e5799d018f311f1bf5cdd5a80e19e142ca/bob/learn/em/cpp/FABaseTrainer.cpp#L325
+ https://gitlab.idiap.ch/bob/bob.learn.em/-/blob/da92d0e5799d018f311f1bf5cdd5a80e19e142ca/bob/learn/em/cpp/FABaseTrainer.cpp#L325
"""
# UProd = (self.ubm.n_gaussians, self.r_U, self.r_U)
@@ -495,10 +497,10 @@ class FactorAnalysisBase(BaseEstimator):
The accumulators are defined as
- :math:`A_1 = \sum\limits_{i=1}^{I}\sum\limits_{h=1}^{H}N_{i,h,c}E(x_{i,h,c} x^{\top}_{i,h,c})`
+ :math:`A_1 = \\sum\\limits_{i=1}^{I}\\sum\\limits_{h=1}^{H}N_{i,h,c}E(x_{i,h,c} x^{\\top}_{i,h,c})`
- :math:`A_2 = \sum\limits_{i=1}^{I}\sum\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \mu_c -D_{c}z_{i,c} -V_{c}y_{i,c} )E[x_{i,h}]^{\top}`
+ :math:`A_2 = \\sum\\limits_{i=1}^{I}\\sum\\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \\mu_c -D_{c}z_{i,c} -V_{c}y_{i,c} )E[x_{i,h}]^{\\top}`
More information, please, check the technical notes attached
@@ -534,7 +536,7 @@ class FactorAnalysisBase(BaseEstimator):
"""
- ## U accumulators
+ # U accumulators
acc_U_A1 = np.zeros((self.ubm.n_gaussians, self.r_U, self.r_U))
acc_U_A2 = np.zeros((self.supervector_dimension, self.r_U))
@@ -568,7 +570,9 @@ class FactorAnalysisBase(BaseEstimator):
return acc_U_A1, acc_U_A2
- #################### Estimating D and z ######################
+ """
+ Estimating D and z
+ """
def update_z(self, X, y, latent_x, latent_y, latent_z, n_acc, f_acc):
"""
@@ -644,7 +648,7 @@ class FactorAnalysisBase(BaseEstimator):
"""
- tmp_CD = np.repeat(n_acc_i, self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_acc_i, self.feature_dimension)
id_plus_d_prod = np.ones(tmp_CD.shape) + dt_inv_sigma_d * tmp_CD
return 1 / id_plus_d_prod
@@ -664,9 +668,9 @@ class FactorAnalysisBase(BaseEstimator):
m = self.mean_supervector
- tmp_CD = np.repeat(n_acc_i, self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_acc_i, self.feature_dimension)
- ## JFA session part
+ # JFA session part
V_dot_v = V @ latent_y_i if latent_y_i is not None else 0
# m_cache_Fn_z_i = Fi - m_tmp_CD * (m + m_tmp_CD_b); // Fn_yi = sum_{sessions h}(N_{i,h}*(o_{i,h} - m - V*y_{i})
@@ -675,7 +679,7 @@ class FactorAnalysisBase(BaseEstimator):
# Looping over the sessions
for session_id in range(len(X_i)):
n_i = X_i[session_id].n
- tmp_CD = np.repeat(n_i, self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_i, self.feature_dimension)
x_i_h = latent_x_i[:, session_id]
fn_z_i -= tmp_CD * (U @ x_i_h)
@@ -690,10 +694,10 @@ class FactorAnalysisBase(BaseEstimator):
The accumulators are defined as
- :math:`A_1 = \sum\limits_{i=1}^{I}E[z_{i,c}z^{\top}_{i,c}]`
+ :math:`A_1 = \\sum\\limits_{i=1}^{I}E[z_{i,c}z^{\\top}_{i,c}]`
- :math:`A_2 = \sum\limits_{i=1}^{I} \Bigg[\sum\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \mu_c -U_{c}x_{i,h,c} -V_{c}y_{i,c} )\Bigg]E[z_{i}]^{\top}`
+ :math:`A_2 = \\sum\\limits_{i=1}^{I} \\Bigg[\\sum\\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \\mu_c -U_{c}x_{i,h,c} -V_{c}y_{i,c} )\\Bigg]E[z_{i}]^{\\top}`
More information, please, check the technical notes attached
@@ -757,7 +761,7 @@ class FactorAnalysisBase(BaseEstimator):
X_i, latent_x_i, latent_y_i, n_acc[y_i], f_acc[y_i]
)
- tmp_CD = np.repeat(n_acc[y_i], self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_acc[y_i], self.feature_dimension)
acc_D_A1 += (
id_plus_d_prod + latent_z[y_i] * latent_z[y_i]
) * tmp_CD
@@ -806,7 +810,9 @@ class FactorAnalysisBase(BaseEstimator):
return latent_x, latent_y, latent_z
- #################### Estimating V and y ######################
+ """
+ Estimating V and y
+ """
def update_y(self, X, y, VProd, latent_x, latent_y, latent_z, n_acc, f_acc):
"""
@@ -874,7 +880,7 @@ class FactorAnalysisBase(BaseEstimator):
"""
- I = np.eye(self.r_V, self.r_V)
+ I = np.eye(self.r_V, self.r_V) # noqa: E741
# TODO: make the invertion matrix function as a parameter
return np.linalg.inv(I + (VProd * n_acc_i[:, None, None]).sum(axis=0))
@@ -884,7 +890,7 @@ class FactorAnalysisBase(BaseEstimator):
Computes V_c.T*inv(Sigma_c) @ V_c.T
- ### https://gitlab.idiap.ch/bob/bob.learn.em/-/blob/da92d0e5799d018f311f1bf5cdd5a80e19e142ca/bob/learn/em/cpp/FABaseTrainer.cpp#L193
+ https://gitlab.idiap.ch/bob/bob.learn.em/-/blob/da92d0e5799d018f311f1bf5cdd5a80e19e142ca/bob/learn/em/cpp/FABaseTrainer.cpp#L193
"""
Vc = self._V.reshape(
@@ -904,10 +910,10 @@ class FactorAnalysisBase(BaseEstimator):
Computes the accumulators for the update of V matrix
The accumulators are defined as
- :math:`A_1 = \sum\limits_{i=1}^{I}E[y_{i,c}y^{\top}_{i,c}]`
+ :math:`A_1 = \\sum\\limits_{i=1}^{I}E[y_{i,c}y^{\\top}_{i,c}]`
- :math:`A_2 = \sum\limits_{i=1}^{I} \Bigg[\sum\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \mu_c -U_{c}x_{i,h,c} -D_{c}z_{i,c} )\Bigg]E[y_{i}]^{\top}`
+ :math:`A_2 = \\sum\\limits_{i=1}^{I} \\Bigg[\\sum\\limits_{h=1}^{H}N_{i,h,c}(o_{i,h} - \\mu_c -U_{c}x_{i,h,c} -D_{c}z_{i,c} )\\Bigg]E[y_{i}]^{\\top}`
More information, please, check the technical notes attached
@@ -951,7 +957,7 @@ class FactorAnalysisBase(BaseEstimator):
"""
- ## U accumulators
+ # U accumulators
acc_V_A1 = np.zeros((self.ubm.n_gaussians, self.r_V, self.r_V))
acc_V_A2 = np.zeros((self.supervector_dimension, self.r_V))
@@ -1024,25 +1030,24 @@ class FactorAnalysisBase(BaseEstimator):
# y = self.y[i] # Not doing JFA
- tmp_CD = np.repeat(n_acc_i, self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_acc_i, self.feature_dimension)
fn_y_i = f_acc_i.flatten() - tmp_CD * (
m - D * latent_z_i
) # Fn_yi = sum_{sessions h}(N_{i,h}*(o_{i,h} - m - D*z_{i})
- ### NOT DOING JFA
-
# Looping over the sessions of a ;ane;
for session_id in range(len(X_i)):
n_i = X_i[session_id].n
U_dot_x = U @ latent_x_i[:, session_id]
- tmp_CD = np.repeat(n_i, self.supervector_dimension // 2)
+ tmp_CD = np.repeat(n_i, self.feature_dimension)
fn_y_i -= tmp_CD * U_dot_x
return fn_y_i
- ####################################################################################################################
- # Scoring
+ """
+ Scoring
+ """
def estimate_x(self, X):
@@ -1064,7 +1069,7 @@ class FactorAnalysisBase(BaseEstimator):
X_i: list of :py:class:`bob.learn.em.GMMStats`
List of statistics for a class
"""
- I = np.eye(self.r_U, self.r_U)
+ I = np.eye(self.r_U, self.r_U) # noqa: E741
Uc = self._U.reshape(
(self.ubm.n_gaussians, self.feature_dimension, self.r_U)
@@ -1072,16 +1077,11 @@ class FactorAnalysisBase(BaseEstimator):
UcT = np.transpose(Uc, axes=(0, 2, 1))
- sigma_c = np.reshape(
- self.variance_supervector,
- (self.ubm.n_gaussians, self.feature_dimension),
- )
+ sigma_c = self.ubm.variances[:, np.newaxis]
n_i_c = np.expand_dims(X_i.n[:, np.newaxis], axis=2)
- id_plus_us_prod_inv = I + (
- ((UcT / sigma_c[:, np.newaxis]) @ Uc) * n_i_c
- ).sum(axis=0)
+ id_plus_us_prod_inv = I + (((UcT / sigma_c) @ Uc) * n_i_c).sum(axis=0)
id_plus_us_prod_inv = np.linalg.inv(id_plus_us_prod_inv)
return id_plus_us_prod_inv
@@ -1135,7 +1135,9 @@ class ISVMachine(FactorAnalysisBase):
"""
- def __init__(self, ubm, r_U, em_iterations, relevance_factor=4.0, seed=0):
+ def __init__(
+ self, ubm, r_U, em_iterations=10, relevance_factor=4.0, seed=0
+ ):
super(ISVMachine, self).__init__(
ubm,
r_U=r_U,
@@ -1206,6 +1208,8 @@ class ISVMachine(FactorAnalysisBase):
if not hasattr(self, "_U") or not hasattr(self, "_D"):
self.create_UVD()
+ y = y.tolist() if not isinstance(y, list) else y
+
# TODO: Point of parallelism
n_acc, f_acc = self.initialize(X, y)
for i in range(self.em_iterations):
@@ -1292,7 +1296,7 @@ class JFAMachine(FactorAnalysisBase):
within-class assumption (modeled with :math:`U`), it also hypothesize that
between class variations are embedded in a low rank rectangular matrix
:math:`V`. In the supervector notation, this modeling has the following shape:
- :math:`\mu_{i, j} = m + Ux_{i, j} + Vy_{i} + D_z{i}`.
+ :math:`\\mu_{i, j} = m + Ux_{i, j} + Vy_{i} + D_z{i}`.
For more information check [McCool2013]_
@@ -1320,7 +1324,7 @@ class JFAMachine(FactorAnalysisBase):
"""
def __init__(
- self, ubm, r_U, r_V, em_iterations, relevance_factor=4.0, seed=0
+ self, ubm, r_U, r_V, em_iterations=10, relevance_factor=4.0, seed=0
):
super(JFAMachine, self).__init__(
ubm,
@@ -1369,7 +1373,7 @@ class JFAMachine(FactorAnalysisBase):
latent_x, latent_y, latent_z = self.initialize_XYZ(y)
- #### UPDATE Y, X AND FINALY Z
+ # UPDATE Y, X AND FINALY Z
latent_y = self.update_y(
X, y, VProd, latent_x, latent_y, latent_z, n_acc, f_acc
@@ -1440,7 +1444,7 @@ class JFAMachine(FactorAnalysisBase):
latent_x, latent_y, latent_z = self.initialize_XYZ(y)
- #### UPDATE Y, X AND FINALY Z
+ # UPDATE Y, X AND FINALY Z
latent_y = self.update_y(
X, y, VProd, latent_x, latent_y, latent_z, n_acc, f_acc
@@ -1680,6 +1684,8 @@ class JFAMachine(FactorAnalysisBase):
):
self.create_UVD()
+ y = y.tolist() if not isinstance(y, list) else y
+
# TODO: Point of parallelism
n_acc, f_acc = self.initialize(X, y)
diff --git a/bob/learn/em/test/test_jfa.py b/bob/learn/em/test/test_jfa.py
index 23086de..c96f59e 100644
--- a/bob/learn/em/test/test_jfa.py
+++ b/bob/learn/em/test/test_jfa.py
@@ -7,8 +7,8 @@
# Copyright (C) 2011-2014 Idiap Research Institute, Martigny, Switzerland
import numpy as np
+
from bob.learn.em import GMMMachine, GMMStats, ISVMachine, JFAMachine
-import copy
def test_JFAMachine():
@@ -97,4 +97,3 @@ def test_ISVMachine():
score_ref = -3.280498193082100
assert abs(score_ref - score) < eps
- pass
diff --git a/bob/learn/em/test/test_jfa_trainer.py b/bob/learn/em/test/test_jfa_trainer.py
index f9e51e4..b4b75b7 100644
--- a/bob/learn/em/test/test_jfa_trainer.py
+++ b/bob/learn/em/test/test_jfa_trainer.py
@@ -6,9 +6,11 @@
#
# Copyright (C) 2011-2014 Idiap Research Institute, Martigny, Switzerland
+import copy
+
import numpy as np
+
from bob.learn.em import GMMMachine, GMMStats, ISVMachine, JFAMachine
-import copy
# Define Training set and initial values for tests
F1 = np.array(
@@ -120,12 +122,11 @@ def test_JFATrainAndEnrol():
ubm.means = UBM_MEAN.reshape((2, 3))
ubm.variances = UBM_VAR.reshape((2, 3))
it = JFAMachine(ubm, 2, 2, em_iterations=10)
- # n_acc, f_acc = it.initialize(TRAINING_STATS_X, TRAINING_STATS_y)
+
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)
- # bob.learn.em.train_jfa(t, mb, TRAINING_STATS, initialize=False)
v_ref = np.array(
[
@@ -211,28 +212,6 @@ def test_JFATrainAndEnrol():
assert np.allclose(latent_y, y_ref, eps)
assert np.allclose(latent_z, z_ref, eps)
- # Testing exceptions
- """
- nose.tools.assert_raises(RuntimeError, t.initialize, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.initialize, mb, [[1, 2, 2]])
- nose.tools.assert_raises(RuntimeError, t.e_step_u, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.e_step_u, mb, [[1, 2, 2]])
- nose.tools.assert_raises(RuntimeError, t.m_step_u, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.m_step_u, mb, [[1, 2, 2]])
-
- nose.tools.assert_raises(RuntimeError, t.e_step_v, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.e_step_v, mb, [[1, 2, 2]])
- nose.tools.assert_raises(RuntimeError, t.m_step_v, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.m_step_v, mb, [[1, 2, 2]])
-
- nose.tools.assert_raises(RuntimeError, t.e_step_d, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.e_step_d, mb, [[1, 2, 2]])
- nose.tools.assert_raises(RuntimeError, t.m_step_d, mb, [1, 2, 2])
- nose.tools.assert_raises(RuntimeError, t.m_step_d, mb, [[1, 2, 2]])
-
- nose.tools.assert_raises(RuntimeError, t.enroll, m, [[1, 2, 2]], 5)
- """
-
def test_ISVTrainAndEnrol():
# Train and enroll an 'ISVMachine'
@@ -272,9 +251,9 @@ def test_ISVTrainAndEnrol():
"float64",
)
- ######################################
- # Calls the train function
- ######################################
+ """
+ Calls the train function
+ """
ubm = GMMMachine(2, 3)
ubm.means = UBM_MEAN.reshape((2, 3))
ubm.variances = UBM_VAR.reshape((2, 3))
@@ -292,9 +271,9 @@ def test_ISVTrainAndEnrol():
assert np.allclose(it.D, d_ref, eps)
assert np.allclose(it.U, u_ref, eps)
- ######################################
- # Calls the enroll function
- ######################################
+ """
+ Calls the enroll function
+ """
Ne = np.array([0.1579, 0.9245, 0.1323, 0.2458]).reshape((2, 2))
Fe = np.array(
@@ -325,13 +304,6 @@ def test_ISVTrainAndEnrol():
latent_z = it.enroll(gse, 5)
assert np.allclose(latent_z, z_ref, eps)
- # Testing exceptions
- # nose.tools.assert_raises(RuntimeError, t.initialize, mb, [1, 2, 2])
- # nose.tools.assert_raises(RuntimeError, t.initialize, mb, [[1, 2, 2]])
- # nose.tools.assert_raises(RuntimeError, t.e_step, mb, [1, 2, 2])
- # nose.tools.assert_raises(RuntimeError, t.e_step, mb, [[1, 2, 2]])
- # nose.tools.assert_raises(RuntimeError, t.enroll, m, [[1, 2, 2]], 5)
-
def test_JFATrainInitialize():
# Check that the initialization is consistent and using the rng (cf. issue #118)
@@ -343,7 +315,7 @@ def test_JFATrainInitialize():
ubm.means = UBM_MEAN.reshape((2, 3))
ubm.variances = UBM_VAR.reshape((2, 3))
- ## JFA
+ # JFA
it = JFAMachine(ubm, 2, 2, em_iterations=10)
# first round
@@ -373,7 +345,7 @@ def test_ISVTrainInitialize():
ubm.means = UBM_MEAN.reshape((2, 3))
ubm.variances = UBM_VAR.reshape((2, 3))
- ## ISV
+ # ISV
it = ISVMachine(ubm, 2, em_iterations=10)
# it.rng = rng
diff --git a/bob/learn/em/wccn.py b/bob/learn/em/wccn.py
index 7c2c824..47d5b80 100644
--- a/bob/learn/em/wccn.py
+++ b/bob/learn/em/wccn.py
@@ -1,3 +1,6 @@
+#!/usr/bin/env python
+# @author: Tiago de Freitas Pereira
+
import dask
# Dask doesn't have an implementation for `pinv`
diff --git a/bob/learn/em/whitening.py b/bob/learn/em/whitening.py
index 3565f4f..bf81a36 100644
--- a/bob/learn/em/whitening.py
+++ b/bob/learn/em/whitening.py
@@ -1,3 +1,6 @@
+#!/usr/bin/env python
+# @author: Tiago de Freitas Pereira
+
import dask
from scipy.linalg import pinv
diff --git a/buildout.cfg b/buildout.cfg
index d3c5cee..044f236 100644
--- a/buildout.cfg
+++ b/buildout.cfg
@@ -8,6 +8,7 @@ eggs = bob.learn.em
extensions = bob.buildout
newest = false
verbose = true
+debug = true
[scripts]
recipe = bob.buildout:scripts
diff --git a/doc/index.rst b/doc/index.rst
index d814131..14a5f1d 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -37,7 +37,9 @@ References
..
.. [Vogt2008] *R. Vogt, S. Sridharan*. **'Explicit Modelling of Session Variability for Speaker Verification'**, Computer Speech & Language, 2008, vol. 22, no. 1, pp. 17-38
..
- .. [McCool2013] *C. McCool, R. Wallace, M. McLaren, L. El Shafey, S. Marcel*. **'Session Variability Modelling for Face Authentication'**, IET Biometrics, 2013
+
+.. [McCool2013] *C. McCool, R. Wallace, M. McLaren, L. El Shafey, S. Marcel*. **'Session Variability Modelling for Face Authentication'**, IET Biometrics, 2013
+
..
.. [ElShafey2014] *Laurent El Shafey, Chris McCool, Roy Wallace, Sebastien Marcel*. **'A Scalable Formulation of Probabilistic Linear Discriminant Analysis: Applied to Face Recognition'**, TPAMI'2014
..
diff --git a/doc/plot/plot_ISV.py b/doc/plot/plot_ISV.py
new file mode 100644
index 0000000..cc7b559
--- /dev/null
+++ b/doc/plot/plot_ISV.py
@@ -0,0 +1,168 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+from sklearn.datasets import load_iris
+
+import bob.learn.em
+
+np.random.seed(2) # FIXING A SEED
+
+
+def isv_train(features, ubm):
+ """
+ Train U matrix
+
+ **Parameters**
+ features: List of :py:class:`bob.learn.em.GMMStats` organized by class
+
+ n_gaussians: UBM (:py:class:`bob.learn.em.GMMMachine`)
+
+ """
+
+ stats = []
+ for user in features:
+ user_stats = []
+ for f in user:
+ s = bob.learn.em.GMMStats(ubm.shape[0], ubm.shape[1])
+ ubm.acc_statistics(f, s)
+ user_stats.append(s)
+ stats.append(user_stats)
+
+ relevance_factor = 4
+ subspace_dimension_of_u = 1
+
+ isvbase = bob.learn.em.ISVBase(ubm, subspace_dimension_of_u)
+ trainer = bob.learn.em.ISVTrainer(relevance_factor)
+ # trainer.rng = bob.core.random.mt19937(int(self.init_seed))
+ bob.learn.em.train(trainer, isvbase, stats, max_iterations=50)
+
+ return isvbase
+
+
+# GENERATING DATA
+iris_data = load_iris()
+X = np.column_stack((iris_data.data[:, 0], iris_data.data[:, 3]))
+y = iris_data.target
+
+setosa = X[iris_data.target == 0]
+versicolor = X[iris_data.target == 1]
+virginica = X[iris_data.target == 2]
+
+n_gaussians = 3
+r_U = 1
+
+
+# TRAINING THE PRIOR
+ubm = bob.learn.em.GMMMachine(n_gaussians)
+# Initializing with old bob initialization
+ubm.means = np.array(
+ [
+ [5.0048631, 0.26047739],
+ [5.83509503, 1.40530362],
+ [6.76257257, 1.98965356],
+ ]
+)
+ubm.variances = np.array(
+ [
+ [0.11311728, 0.05183813],
+ [0.11587106, 0.08492455],
+ [0.20482993, 0.10438209],
+ ]
+)
+
+ubm.weights = np.array([0.36, 0.36, 0.28])
+
+gmm_stats = [ubm.acc_statistics(x[np.newaxis]) for x in X]
+isv_machine = bob.learn.em.ISVMachine(ubm, r_U, em_iterations=50)
+isv_machine.U = np.array(
+ [[-0.150035, -0.44441, -1.67812, 2.47621, -0.52885, 0.659141]]
+).T
+
+isv_machine = isv_machine.fit(gmm_stats, y)
+
+# gmm_stats = [ubm.acc_statistics(x) for x in [setosa, versicolor, virginica]]
+# isv_machine = bob.learn.em.ISVMachine(ubm, r_U).fit(gmm_stats, [0, 1, 2])
+
+
+# isvbase = isv_train([setosa, versicolor, virginica], ubm)
+
+# Variability direction
+u0 = isv_machine.U[0:2, 0] / np.linalg.norm(isv_machine.U[0:2, 0])
+u1 = isv_machine.U[2:4, 0] / np.linalg.norm(isv_machine.U[2:4, 0])
+u2 = isv_machine.U[4:6, 0] / np.linalg.norm(isv_machine.U[4:6, 0])
+
+figure, ax = plt.subplots()
+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(
+ ubm.means[:, 0],
+ ubm.means[:, 1],
+ c="blue",
+ marker="x",
+ label="centroids - mle",
+)
+# plt.scatter(ubm.means[:, 0], ubm.means[:, 1], c="blue",
+# marker=".", label="within class varibility", s=0.01)
+
+ax.arrow(
+ ubm.means[0, 0],
+ ubm.means[0, 1],
+ u0[0],
+ u0[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[1, 0],
+ ubm.means[1, 1],
+ u1[0],
+ u1[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[2, 0],
+ ubm.means[2, 1],
+ u2[0],
+ u2[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+plt.text(
+ ubm.means[0, 0] + u0[0],
+ ubm.means[0, 1] + u0[1] - 0.1,
+ r"$\mathbf{U}_1$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[1, 0] + u1[0],
+ ubm.means[1, 1] + u1[1] - 0.1,
+ r"$\mathbf{U}_2$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[2, 0] + u2[0],
+ ubm.means[2, 1] + u2[1] - 0.1,
+ r"$\mathbf{U}_3$",
+ fontsize=15,
+)
+
+plt.xticks([], [])
+plt.yticks([], [])
+
+# plt.grid(True)
+plt.xlabel("Sepal length")
+plt.ylabel("Petal width")
+plt.legend()
+plt.tight_layout()
+plt.show()
diff --git a/doc/plot/plot_JFA.py b/doc/plot/plot_JFA.py
new file mode 100644
index 0000000..5c19474
--- /dev/null
+++ b/doc/plot/plot_JFA.py
@@ -0,0 +1,240 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+from sklearn.datasets import load_iris
+
+import bob.learn.em
+
+np.random.seed(2) # FIXING A SEED
+
+
+def isv_train(features, ubm):
+ """
+ Train U matrix
+
+ **Parameters**
+ features: List of :py:class:`bob.learn.em.GMMStats` organized by class
+
+ n_gaussians: UBM (:py:class:`bob.learn.em.GMMMachine`)
+
+ """
+
+ stats = []
+ for user in features:
+ user_stats = []
+ for f in user:
+ s = bob.learn.em.GMMStats(ubm.shape[0], ubm.shape[1])
+ ubm.acc_statistics(f, s)
+ user_stats.append(s)
+ stats.append(user_stats)
+
+ relevance_factor = 4
+ subspace_dimension_of_u = 1
+
+ isvbase = bob.learn.em.ISVBase(ubm, subspace_dimension_of_u)
+ trainer = bob.learn.em.ISVTrainer(relevance_factor)
+ # trainer.rng = bob.core.random.mt19937(int(self.init_seed))
+ bob.learn.em.train(trainer, isvbase, stats, max_iterations=50)
+
+ return isvbase
+
+
+# GENERATING DATA
+iris_data = load_iris()
+X = np.column_stack((iris_data.data[:, 0], iris_data.data[:, 3]))
+y = iris_data.target
+
+
+setosa = X[iris_data.target == 0]
+versicolor = X[iris_data.target == 1]
+virginica = X[iris_data.target == 2]
+
+n_gaussians = 3
+r_U = 1
+r_V = 1
+
+
+# TRAINING THE PRIOR
+ubm = bob.learn.em.GMMMachine(n_gaussians)
+# Initializing with old bob initialization
+ubm.means = np.array(
+ [
+ [5.0048631, 0.26047739],
+ [5.83509503, 1.40530362],
+ [6.76257257, 1.98965356],
+ ]
+)
+ubm.variances = np.array(
+ [
+ [0.11311728, 0.05183813],
+ [0.11587106, 0.08492455],
+ [0.20482993, 0.10438209],
+ ]
+)
+
+ubm.weights = np.array([0.36, 0.36, 0.28])
+# .fit(X)
+
+gmm_stats = [ubm.acc_statistics(x[np.newaxis]) for x in X]
+jfa_machine = bob.learn.em.JFAMachine(ubm, r_U, r_V, em_iterations=50)
+
+# Initializing with old bob initialization
+jfa_machine.U = np.array(
+ [[-0.150035, -0.44441, -1.67812, 2.47621, -0.52885, 0.659141]]
+).T
+
+jfa_machine.Y = np.array(
+ [[-0.538446, 1.67376, -0.111288, 2.06948, 1.39563, -1.65004]]
+).T
+jfa_machine.D = np.array(
+ [0.732467, 0.281321, 0.543212, -0.512974, 1.04108, 0.835224]
+)
+jfa_machine = jfa_machine.fit(gmm_stats, y)
+
+
+# .fit(gmm_stats, y)
+
+# gmm_stats = [ubm.acc_statistics(x) for x in [setosa, versicolor, virginica]]
+# jfa_machine = bob.learn.em.JFAMachine(ubm, r_U, r_V).fit(gmm_stats, [0, 1, 2])
+
+
+# Variability direction U
+u0 = jfa_machine.U[0:2, 0] / np.linalg.norm(jfa_machine.U[0:2, 0])
+u1 = jfa_machine.U[2:4, 0] / np.linalg.norm(jfa_machine.U[2:4, 0])
+u2 = jfa_machine.U[4:6, 0] / np.linalg.norm(jfa_machine.U[4:6, 0])
+
+
+# Variability direction V
+v0 = jfa_machine.V[0:2, 0] / np.linalg.norm(jfa_machine.V[0:2, 0])
+v1 = jfa_machine.V[2:4, 0] / np.linalg.norm(jfa_machine.V[2:4, 0])
+v2 = jfa_machine.V[4:6, 0] / np.linalg.norm(jfa_machine.V[4:6, 0])
+
+
+figure, ax = plt.subplots()
+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(
+ ubm.means[:, 0],
+ ubm.means[:, 1],
+ c="blue",
+ marker="x",
+ label="centroids - mle",
+)
+# plt.scatter(ubm.means[:, 0], ubm.means[:, 1], c="blue",
+# marker=".", label="within class varibility", s=0.01)
+
+# U
+ax.arrow(
+ ubm.means[0, 0],
+ ubm.means[0, 1],
+ u0[0],
+ u0[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[1, 0],
+ ubm.means[1, 1],
+ u1[0],
+ u1[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[2, 0],
+ ubm.means[2, 1],
+ u2[0],
+ u2[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+plt.text(
+ ubm.means[0, 0] + u0[0],
+ ubm.means[0, 1] + u0[1] - 0.1,
+ r"$\mathbf{U}_1$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[1, 0] + u1[0],
+ ubm.means[1, 1] + u1[1] - 0.1,
+ r"$\mathbf{U}_2$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[2, 0] + u2[0],
+ ubm.means[2, 1] + u2[1] - 0.1,
+ r"$\mathbf{U}_3$",
+ fontsize=15,
+)
+
+# V
+ax.arrow(
+ ubm.means[0, 0],
+ ubm.means[0, 1],
+ v0[0],
+ v0[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[1, 0],
+ ubm.means[1, 1],
+ v1[0],
+ v1[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+ax.arrow(
+ ubm.means[2, 0],
+ ubm.means[2, 1],
+ v2[0],
+ v2[1],
+ fc="k",
+ ec="k",
+ head_width=0.05,
+ head_length=0.1,
+)
+plt.text(
+ ubm.means[0, 0] + v0[0],
+ ubm.means[0, 1] + v0[1] - 0.1,
+ r"$\mathbf{V}_1$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[1, 0] + v1[0],
+ ubm.means[1, 1] + v1[1] - 0.1,
+ r"$\mathbf{V}_2$",
+ fontsize=15,
+)
+plt.text(
+ ubm.means[2, 0] + v2[0],
+ ubm.means[2, 1] + v2[1] - 0.1,
+ r"$\mathbf{V}_3$",
+ fontsize=15,
+)
+
+plt.xticks([], [])
+plt.yticks([], [])
+
+plt.xlabel("Sepal length")
+plt.ylabel("Petal width")
+plt.legend(loc=2)
+plt.ylim([-1, 3.5])
+
+plt.tight_layout()
+plt.grid(True)
+plt.show()
--
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