gtlvq

examples/gtlvq_mnist.py

@@ -0,0 +1,165 @@
+"""
+ProtoTorch GTLVQ example using MNIST data.
+The GTLVQ is placed as an classification model on 
+top of a CNN, considered as featurer extractor.
+Initialization of subpsace and prototypes in 
+Siamnese fashion
+For more info about GTLVQ see:
+DOI:10.1109/IJCNN.2016.7727534
+"""
+import sys
+
+from torch.nn import parameter
+from matplotlib.pyplot import fill
+import numpy as np
+import torch
+import torch.nn as nn
+import torchvision
+from torchvision import transforms
+from prototorch.modules.losses import GLVQLoss
+from prototorch.functions.helper import calculate_prototype_accuracy
+from prototorch.modules.models import GTLVQ
+
+# Parameters and options
+n_epochs = 50
+batch_size_train = 64
+batch_size_test = 1000
+learning_rate = 0.1
+momentum = 0.5
+log_interval = 10
+cuda = "cuda:1"
+random_seed = 1
+device = torch.device(cuda if torch.cuda.is_available() else 'cpu')
+
+# Configures reproducability
+torch.manual_seed(random_seed)
+np.random.seed(random_seed)
+
+# Prepare and preprocess the data
+train_loader = torch.utils.data.DataLoader(torchvision.datasets.MNIST(
+    './files/',
+    train=True,
+    download=True,
+    transform=torchvision.transforms.Compose(
+        [transforms.ToTensor(),
+         transforms.Normalize((0.1307, ), (0.3081, ))])),
+                                           batch_size=batch_size_train,
+                                           shuffle=True)
+
+test_loader = torch.utils.data.DataLoader(torchvision.datasets.MNIST(
+    './files/',
+    train=False,
+    download=True,
+    transform=torchvision.transforms.Compose(
+        [transforms.ToTensor(),
+         transforms.Normalize((0.1307, ), (0.3081, ))])),
+                                          batch_size=batch_size_test,
+                                          shuffle=True)
+
+
+# Define the GLVQ model plus appropriate feature extractor
+class CNNGTLVQ(torch.nn.Module):
+    def __init__(
+        self,
+        num_classes,
+        subspace_data,
+        prototype_data,
+        tangent_projection_type="local",
+        prototypes_per_class=2,
+        bottleneck_dim=128,
+    ):
+        super(CNNGTLVQ, self).__init__()
+
+        #Feature Extractor - Simple CNN
+        self.fe = nn.Sequential(nn.Conv2d(1, 32, 3, 1), nn.ReLU(),
+                                nn.Conv2d(32, 64, 3, 1), nn.ReLU(),
+                                nn.MaxPool2d(2), nn.Dropout(0.25),
+                                nn.Flatten(), nn.Linear(9216, bottleneck_dim),
+                                nn.Dropout(0.5), nn.LeakyReLU(),
+                                nn.LayerNorm(bottleneck_dim))
+
+        # Forward pass of subspace and prototype initialization data through feature extractor
+        subspace_data = self.fe(subspace_data)
+        prototype_data[0] = self.fe(prototype_data[0])
+
+        # Initialization of GTLVQ
+        self.gtlvq = GTLVQ(num_classes,
+                           subspace_data,
+                           prototype_data,
+                           tangent_projection_type=tangent_projection_type,
+                           feature_dim=bottleneck_dim,
+                           prototypes_per_class=prototypes_per_class)
+
+    def forward(self, x):
+        # Feature Extraction
+        x = self.fe(x)
+
+        # GTLVQ Forward pass
+        dis = self.gtlvq(x)
+        return dis
+
+
+# Get init data
+subspace_data = torch.cat(
+    [next(iter(train_loader))[0],
+     next(iter(test_loader))[0]])
+prototype_data = next(iter(train_loader))
+
+# Build the CNN GTLVQ  model
+model = CNNGTLVQ(10,
+                 subspace_data,
+                 prototype_data,
+                 tangent_projection_type="local",
+                 bottleneck_dim=128).to(device)
+
+# Optimize using SGD optimizer from `torch.optim`
+optimizer = torch.optim.Adam([{
+    'params': model.fe.parameters()
+}, {
+    'params': model.gtlvq.parameters()
+}],
+                             lr=learning_rate)
+criterion = GLVQLoss(squashing='sigmoid_beta', beta=10)
+
+# Training loop
+for epoch in range(n_epochs):
+    for batch_idx, (x_train, y_train) in enumerate(train_loader):
+        model.train()
+        x_train, y_train = x_train.to(device), y_train.to(device)
+        optimizer.zero_grad()
+
+        distances = model(x_train)
+        plabels = model.gtlvq.cls.prototype_labels.to(device)
+
+        # Compute loss.
+        loss = criterion([distances, plabels], y_train)
+        loss.backward()
+        optimizer.step()
+
+        # GTLVQ uses projected SGD, which means to orthogonalize the subspaces after every gradient update.
+        model.gtlvq.orthogonalize_subspace()
+
+        if batch_idx % log_interval == 0:
+            acc = calculate_prototype_accuracy(distances, y_train, plabels)
+            print(
+                f'Epoch: {epoch + 1:02d}/{n_epochs:02d} Epoch Progress: {100. * batch_idx / len(train_loader):02.02f} % Loss: {loss.item():02.02f} \
+              Train Acc: {acc.item():02.02f}')
+
+    # Test
+    with torch.no_grad():
+        model.eval()
+        correct = 0
+        total = 0
+        for x_test, y_test in test_loader:
+            x_test, y_test = x_test.to(device), y_test.to(device)
+            test_distances = model(torch.tensor(x_test))
+            test_plabels = model.gtlvq.cls.prototype_labels.to(device)
+            i = torch.argmin(test_distances, 1)
+            correct += torch.sum(y_test == test_plabels[i])
+            total += y_test.size(0)
+        print('Accuracy of the network on the test images: %d %%' %
+              (torch.true_divide(correct, total) * 100))
+
+# Save the model
+PATH = './glvq_mnist_model.pth'
+torch.save(model.state_dict(), PATH)

prototorch/functions/distances.py

@@ -1,6 +1,8 @@
 """ProtoTorch distance functions."""
 
 import torch
+from prototorch.functions.helper import equal_int_shape, _int_and_mixed_shape, _check_shapes
+import numpy as np
 
 
 def squared_euclidean_distance(x, y):
@@ -71,5 +73,155 @@ def lomega_distance(x, y, omegas):
     return distances
 
 
+def euclidean_distance_matrix(x, y, squared=False, epsilon=1e-10):
+    r""" Computes an euclidean distanes matrix given two distinct vectors.
+    last dimension must be the vector dimension!
+    compute the distance via the identity of the dot product. This avoids the memory overhead due to the subtraction!
+    
+    x.shape = (number_of_x_vectors, vector_dim)
+    y.shape = (number_of_y_vectors, vector_dim)
+    
+    output: matrix of distances (number_of_x_vectors, number_of_y_vectors)
+    """
+    for tensor in [x, y]:
+        if tensor.ndim != 2:
+            raise ValueError(
+                'The tensor dimension must be two. You provide: tensor.ndim=' +
+                str(tensor.ndim) + '.')
+    if not equal_int_shape([tuple(x.shape)[1]], [tuple(y.shape)[1]]):
+        raise ValueError(
+            'The vector shape must be equivalent in both tensors. You provide: tuple(y.shape)[1]='
+            + str(tuple(x.shape)[1]) + ' and  tuple(y.shape)(y)[1]=' +
+            str(tuple(y.shape)[1]) + '.')
+
+    y = torch.transpose(y)
+
+    diss = torch.sum(x**2, axis=1,
+                     keepdims=True) - 2 * torch.dot(x, y) + torch.sum(
+                         y**2, axis=0, keepdims=True)
+
+    if not squared:
+        if epsilon == 0:
+            diss = torch.sqrt(diss)
+        else:
+            diss = torch.sqrt(torch.max(diss, epsilon))
+
+    return diss
+
+
+def tangent_distance(signals, protos, subspaces, squared=False, epsilon=1e-10):
+    r""" Tangent distances based on the tensorflow implementation of Sascha Saralajews
+    For more info about Tangen distances see DOI:10.1109/IJCNN.2016.7727534.
+    The subspaces is always assumed as transposed and must be orthogonal!
+    For local non sparse signals subspaces must be provided!
+    shape(signals): batch x proto_number x channels x dim1 x dim2 x ... x dimN
+    shape(protos): proto_number x dim1 x dim2 x ... x dimN
+    shape(subspaces): (optional [proto_number]) x prod(dim1 * dim2 * ... * dimN)  x prod(projected_atom_shape)
+    subspace should be orthogonalized
+    Pytorch implementation of Sascha Saralajew's tensorflow code.
+    Translation by Christoph Raab
+    """
+    signal_shape, signal_int_shape = _int_and_mixed_shape(signals)
+    proto_shape, proto_int_shape = _int_and_mixed_shape(protos)
+    subspace_int_shape = tuple(subspaces.shape)
+
+    # check if the shapes are correct
+    _check_shapes(signal_int_shape, proto_int_shape)
+
+    atom_axes = list(range(3, len(signal_int_shape)))
+    # for sparse signals, we use the memory efficient implementation
+    if signal_int_shape[1] == 1:
+        signals = torch.reshape(signals, [-1, np.prod(signal_shape[3:])])
+
+        if len(atom_axes) > 1:
+            protos = torch.reshape(protos, [proto_shape[0], -1])
+
+        if subspaces.ndim == 2:
+            # clean solution without map if the matrix_scope is global
+            projectors = torch.eye(subspace_int_shape[-2]) - torch.dot(
+                subspaces, torch.transpose(subspaces))
+
+            projected_signals = torch.dot(signals, projectors)
+            projected_protos = torch.dot(protos, projectors)
+
+            diss = euclidean_distance_matrix(projected_signals,
+                                             projected_protos,
+                                             squared=squared,
+                                             epsilon=epsilon)
+
+            diss = torch.reshape(
+                diss, [signal_shape[0], signal_shape[2], proto_shape[0]])
+
+            return torch.permute(diss, [0, 2, 1])
+
+        else:
+
+            # no solution without map possible --> memory efficient but slow!
+            projectors = torch.eye(subspace_int_shape[-2]) - torch.bmm(
+                subspaces,
+                subspaces)  #K.batch_dot(subspaces, subspaces, [2, 2])
+
+            projected_protos = (protos @ subspaces
+                                ).T  #K.batch_dot(projectors, protos, [1, 1]))
+
+            def projected_norm(projector):
+                return torch.sum(torch.dot(signals, projector)**2, axis=1)
+
+            diss = torch.transpose(map(projected_norm, projectors)) \
+                    - 2 * torch.dot(signals, projected_protos) \
+                    + torch.sum(projected_protos**2, axis=0, keepdims=True)
+
+            if not squared:
+                if epsilon == 0:
+                    diss = torch.sqrt(diss)
+                else:
+                    diss = torch.sqrt(torch.max(diss, epsilon))
+
+            diss = torch.reshape(
+                diss, [signal_shape[0], signal_shape[2], proto_shape[0]])
+
+            return torch.permute(diss, [0, 2, 1])
+
+    else:
+        signals = signals.permute([0, 2, 1] + atom_axes)
+
+        diff = signals - protos
+
+        # global tangent space
+        if subspaces.ndim == 2:
+            #Scope Projectors
+            projectors = subspaces  #
+
+            #Scope: Tangentspace Projections
+            diff = torch.reshape(
+                diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1))
+            projected_diff = diff @ projectors
+            projected_diff = torch.reshape(
+                projected_diff,
+                (signal_shape[0], signal_shape[2], signal_shape[1]) +
+                signal_shape[3:])
+
+            diss = torch.norm(projected_diff, 2, dim=-1)
+            return diss.permute([0, 2, 1])
+
+        # local tangent spaces
+        else:
+            # Scope: Calculate Projectors
+            projectors = subspaces
+
+            # Scope: Tangentspace Projections
+            diff = torch.reshape(
+                diff, (signal_shape[0] * signal_shape[2], signal_shape[1], -1))
+            diff = diff.permute([1, 0, 2])
+            projected_diff = torch.bmm(diff, projectors)
+            projected_diff = torch.reshape(
+                projected_diff,
+                (signal_shape[1], signal_shape[0], signal_shape[2]) +
+                signal_shape[3:])
+
+            diss = torch.norm(projected_diff, 2, dim=-1)
+            return diss.permute([1, 0, 2]).squeeze(-1)
+
+
 # Aliases
 sed = squared_euclidean_distance

prototorch/functions/helper.py

@@ -0,0 +1,89 @@
+import torch
+
+
+def calculate_prototype_accuracy(y_pred, y_true, plabels):
+    """Computes the accuracy of a prototype based model.
+    via Winner-Takes-All rule.
+    Requirement:
+    y_pred.shape == y_true.shape
+    unique(y_pred) in plabels
+    """
+    with torch.no_grad():
+        idx = torch.argmin(y_pred, axis=1)
+        return torch.true_divide(torch.sum(y_true == plabels[idx]),
+                                 len(y_pred)) * 100
+
+
+def predict_label(y_pred, plabels):
+    r""" Predicts labels given a prediction of a prototype based model. 
+    """
+    with torch.no_grad():
+        return plabels[torch.argmin(y_pred, 1)]
+
+
+def mixed_shape(inputs):
+    if not torch.is_tensor(inputs):
+        raise ValueError('Input must be a tensor.')
+    else:
+        int_shape = list(inputs.shape)
+        # sometimes int_shape returns mixed integer types
+        int_shape = [int(i) if i is not None else i for i in int_shape]
+        tensor_shape = inputs.shape
+
+        for i, s in enumerate(int_shape):
+            if s is None:
+                int_shape[i] = tensor_shape[i]
+        return tuple(int_shape)
+
+
+def equal_int_shape(shape_1, shape_2):
+    if not isinstance(shape_1,
+                      (tuple, list)) or not isinstance(shape_2, (tuple, list)):
+        raise ValueError('Input shapes must list or tuple.')
+    for shape in [shape_1, shape_2]:
+        if not all([isinstance(x, int) or x is None for x in shape]):
+            raise ValueError(
+                'Input shapes must be list or tuple of int and None values.')
+
+    if len(shape_1) != len(shape_2):
+        return False
+    else:
+        for axis, value in enumerate(shape_1):
+            if value is not None and shape_2[axis] not in {value, None}:
+                return False
+        return True
+
+
+def _check_shapes(signal_int_shape, proto_int_shape):
+    if len(signal_int_shape) < 4:
+        raise ValueError(
+            "The number of signal dimensions must be >=4. You provide: " +
+            str(len(signal_int_shape)))
+
+    if len(proto_int_shape) < 2:
+        raise ValueError(
+            "The number of proto dimensions must be >=2. You provide: " +
+            str(len(proto_int_shape)))
+
+    if not equal_int_shape(signal_int_shape[3:], proto_int_shape[1:]):
+        raise ValueError(
+            "The atom shape of signals must be equal protos. You provide: signals.shape[3:]="
+            + str(signal_int_shape[3:]) + " != protos.shape[1:]=" +
+            str(proto_int_shape[1:]))
+
+    # not a sparse signal
+    if signal_int_shape[1] != 1:
+        if not equal_int_shape(signal_int_shape[1:2], proto_int_shape[0:1]):
+            raise ValueError(
+                "If the signal is not sparse, the number of prototypes must be equal in signals and "
+                "protos. You provide: " + str(signal_int_shape[1]) + " != " +
+                str(proto_int_shape[0]))
+
+    return True
+
+
+def _int_and_mixed_shape(tensor):
+    shape = mixed_shape(tensor)
+    int_shape = tuple([i if isinstance(i, int) else None for i in shape])
+
+    return shape, int_shape

prototorch/functions/normalization.py

@@ -0,0 +1,37 @@
+# -*- coding: utf-8 -*-
+from __future__ import print_function
+from __future__ import absolute_import
+from __future__ import division
+
+import torch
+
+
+def orthogonalization(tensors):
+    r""" Orthogonalization of a given tensor via polar decomposition.
+    """
+    u, _, v = torch.svd(tensors, compute_uv=True)
+    u_shape = tuple(list(u.shape))
+    v_shape = tuple(list(v.shape))
+
+    # reshape to (num x N x M)
+    u = torch.reshape(u, (-1, u_shape[-2], u_shape[-1]))
+    v = torch.reshape(v, (-1, v_shape[-2], v_shape[-1]))
+
+    out = u @ v.permute([0, 2, 1])
+
+    out = torch.reshape(out, u_shape[:-1] + (v_shape[-2], ))
+
+    return out
+
+
+def trace_normalization(tensors, epsilon=[1e-10]):
+    r""" Trace normalization
+    """
+    epsilon = torch.tensor([1e-10], dtype=torch.float64)
+    # Scope trace_normalization
+    constant = torch.trace(tensors)
+
+    if epsilon != 0:
+        constant = torch.max(constant, epsilon)
+
+    return tensors / constant

prototorch/modules/models.py

@@ -0,0 +1,190 @@
+from torch import nn
+import torch
+from prototorch.modules.prototypes import Prototypes1D
+from prototorch.functions.distances import tangent_distance, euclidean_distance_matrix
+from prototorch.functions.normalization import orthogonalization
+from prototorch.functions.helper import _check_shapes,_int_and_mixed_shape
+
+class GTLVQ(nn.Module):
+    r""" Generalized Tangent Learning Vector Quantization
+
+    Parameters
+    ----------
+    num_classes: int 
+        Number of classes of the given classification problem.
+
+    subspace_data: torch.tensor of shape (n_batch,feature_dim,feature_dim)
+        Subspace data for the point approximation, required
+
+    prototype_data: torch.tensor of shape (n_init_data,feature_dim) (optional)
+        prototype data for initalization of the prototypes used in GTLVQ.
+
+    tangent_projection_type: string 
+        Specifies the tangent projection type
+        options:    local
+                    local_proj
+                    global
+        local: computes the tangent distances without emphasizing projected
+        data. Only distances are available
+        local_proj: computs tangent distances and returns the projected data
+        for further use. Be careful: data is repeated by number of prototypes
+        global: Number of subspaces is set to one and every prototypes 
+        uses the same. 
+    
+    prototypes_per_class: int (default=2,optional)
+    Number of prototypes per class
+
+    feature_dim: int (default=256)
+    Dimensionality of the feature space specified as integer. 
+    Prototype dimension. 
+
+    Notes
+    -----
+    The GTLVQ [1] is a prototype-based classification learning model. The 
+    GTLVQ uses the Tangent-Distances for a local point approximation 
+    of an assumed data manifold via prototypial representations. 
+
+    The GTLVQ requires subspace projectors for transforming the data
+    and prototypes into the affine subspace. Every prototype is 
+    equipped with a specific subpspace and represents a point 
+    approximation of the assumed manifold.
+
+    In practice prototypes and data are projected on this manifold 
+    and pairwise euclidean distance computes.
+
+    References
+    ----------
+    .. [1] Saralajew, Sascha; Villmann, Thomas: Transfer learning 
+    in classification based on manifolc. models and its relation
+    to tangent metric learning. In: 2017 International Joint
+    Conference on Neural Networks (IJCNN).
+    Bd. 2017-May : IEEE, 2017, S. 1756–1765
+    """
+    def __init__(
+        self,
+        num_classes,
+        subspace_data=None,
+        prototype_data=None,
+        subspace_size=256,
+        tangent_projection_type='local',
+        prototypes_per_class=2,
+        feature_dim=256,
+    ):
+        super(GTLVQ, self).__init__()
+
+        self.num_protos = num_classes * prototypes_per_class
+        self.subspace_size = feature_dim if subspace_size is None else subspace_size
+        self.feature_dim = feature_dim
+
+        if subspace_data is None:
+            raise ValueError('Init Data must be specified!')
+
+        self.tpt = tangent_projection_type
+        with torch.no_grad():
+            if self.tpt == 'local' or self.tpt == 'local_proj':
+                self.subspaces = torch.nn.Parameter(
+                    self.init_local_subspace(
+                        subspace_data).clone().detach().requires_grad_(True))
+            elif self.tpt == 'global':
+                self.subspaces = torch.nn.Parameter(
+                    self.init_gobal_subspace(
+                        subspace_data).clone().detach().requires_grad_(True))
+            else:
+                self.subspaces = None
+
+        # Hypothesis-Margin-Classifier
+        self.cls = Prototypes1D(input_dim=feature_dim,
+                                prototypes_per_class=prototypes_per_class,
+                                nclasses=num_classes,
+                                prototype_initializer='stratified_mean',
+                                data=prototype_data)
+
+    def forward(self, x):
+        # Tangent Projection
+        if self.tpt == 'local_proj':
+            x_conform = x.unsqueeze(1).repeat_interleave(self.num_protos,
+                                                         1).unsqueeze(2)
+            dis, proj_x = self.local_tangent_projection(
+                x_conform, self.cls.prototypes, self.subspaces)
+            proj_x = proj_x.reshape(x.shape[0] * self.num_protos,
+                                    self.feature_dim)
+            return proj_x, dis
+        elif self.tpt == "local":
+            x_conform = x.unsqueeze(1).repeat_interleave(self.num_protos,
+                                                         1).unsqueeze(2)
+            dis = tangent_distance(x_conform, self.cls.prototypes,
+                                   self.subspaces)
+        elif self.tpt == "gloabl":
+            dis = self.global_tangent_distances(x)
+        else:
+            dis = (x @ self.cls.prototypes.T) / (
+                torch.norm(x, dim=1, keepdim=True) @ torch.norm(
+                    self.cls.prototypes, dim=1, keepdim=True).T)
+        return dis
+
+    def init_gobal_subspace(self, data, num_subspaces):
+        _, _, v = torch.svd(data)
+        subspace = (torch.eye(v.shape[0]) - (v @ v.T)).T
+        return subspace[:, :num_subspaces]
+
+    def init_local_subspace(self, data):
+        _, _, v = torch.svd(data)
+        inital_projector = (torch.eye(v.shape[0]) - (v @ v.T)).T
+        return inital_projector.unsqueeze(0).repeat_interleave(
+            self.num_protos, 0)
+
+    def global_tangent_distances(self, x):
+        # Tangent Projection
+        x, projected_prototypes = x @ self.subspaces, self.cls.prototypes @ self.subspaces
+        # Euclidean Distance
+        return euclidean_distance_matrix(x, projected_prototypes)
+
+    def local_tangent_projection(self,
+                                 signals,
+                                 protos,
+                                 subspaces,
+                                 squared=False,
+                                 epsilon=1e-10):
+        # Note: subspaces is always assumed as transposed and must be orthogonal!
+        # shape(signals): batch x proto_number x channels x dim1 x dim2 x ... x dimN
+        # shape(protos): proto_number x dim1 x dim2 x ... x dimN
+        # shape(subspaces): (optional [proto_number]) x prod(dim1 * dim2 * ... * dimN)  x prod(projected_atom_shape)
+        # subspace should be orthogonalized
+        # Origin Source Code
+        # Origin Author:
+
+        signal_shape, signal_int_shape = _int_and_mixed_shape(signals)
+        proto_shape, proto_int_shape = _int_and_mixed_shape(protos)
+
+        # check if the shapes are correct
+        _check_shapes(signal_int_shape, proto_int_shape)
+
+        atom_axes = list(range(3, len(signal_int_shape)))
+
+        # Tangent Data Projections
+        projected_protos = torch.bmm(protos.unsqueeze(1), subspaces).squeeze(1)
+        data = signals.squeeze(2).permute([1, 0, 2])
+        projected_data = torch.bmm(data, subspaces)
+        projected_data = projected_data.permute([1, 0, 2]).unsqueeze(1)
+        diff = projected_data - projected_protos
+        projected_diff = torch.reshape(
+            diff, (signal_shape[1], signal_shape[0], signal_shape[2]) +
+            signal_shape[3:])
+        diss = torch.norm(projected_diff,2,dim=-1)
+        return diss.permute([1, 0, 2]).squeeze(-1), projected_data.squeeze(1)
+
+    def get_parameters(self):
+        return {
+            "params": self.cls.prototypes,
+        }, {
+            "params": self.subspaces
+        }
+
+    def orthogonalize_subspace(self):
+        if self.subspaces is not None:
+            with torch.no_grad():
+                ortho_subpsaces = orthogonalization(
+                    self.subspaces
+                ) if self.tpt == 'global' else torch.nn.init.orthogonal_(
+                    self.subspaces)
+                self.subspaces.copy_(ortho_subpsaces)