We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from topological data analysis, to capture high-level topological characteristics of segmentation results in a way which is differentiable with respect to the pixelwise probability of being assigned to a given class. The topological prior knowledge consists of the sequence of desired Betti numbers of the segmentation. As a proof-of-concept we demonstrate our approach by applying it to the problem of left-ventricle segmentation of cardiac MR images of 500 subjects from the UK Biobank dataset, where we show that it improves segmentation performance in terms of topological correctness without sacrificing pixelwise accuracy.
The recent work of @cite_2 introduced a topological regulariser for classification problems by considering the stability of connected components of the classification boundary and can be extended to higher-order topological features. It also provided a differentiable loss function which can be incorporated in the training of a neural network. This approach differs from ours in that firstly, it imposes topological constraints on the shape of the classification boundary in the feature space of inputs to the network, rather than topological constraints in the space of the pixels in the image, and secondly it aims only to reduce overall topological complexity. Our approach aims to fit the desired absence or presence of certain features and so complex features can be penalised or rewarded, as is appropriate for the task at hand.
@cite_2
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Regularization plays a crucial role in supervised learning. A successfully regularized model strikes a balance between a perfect description of the training data and the ability to generalize to unseen data. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of the classification boundary by regularizing over its topological complexity. In particular, our measurement of topological complexity incorporates the importance of topological features (e.g., connected components, handles, and so on) in a meaningful manner, and provides a direct control over spurious topological structures. We incorporate the new measurement as a topological loss in training classifiers. We also propose an efficient algorithm to compute the gradient. Our method provides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model. We demonstrate the effectiveness of our new topological regularizer on a range of synthetic and real-world datasets. We present a method for transferring neural representations from label-rich source domains to unlabeled target domains. Recent adversarial methods proposed for this task learn to align features across domains by fooling a special domain critic network. However, a drawback of this approach is that the critic simply labels the generated features as in-domain or not, without considering the boundaries between classes. This can lead to ambiguous features being generated near class boundaries, reducing target classification accuracy. We propose a novel approach, Adversarial Dropout Regularization (ADR), to encourage the generator to output more discriminative features for the target domain. Our key idea is to replace the critic with one that detects non-discriminative features, using dropout on the classifier network. The generator then learns to avoid these areas of the feature space and thus creates better features. We apply our ADR approach to the problem of unsupervised domain adaptation for image classification and semantic segmentation tasks, and demonstrate significant improvement over the state of the art. We also show that our approach can be used to train Generative Adversarial Networks for semi-supervised learning. We present a method for transferring neural representations from label-rich source domains to unlabeled target domains. Recent adversarial methods proposed for this task learn to align features across domains by fooling a special domain critic network. However, a drawback of this approach is that the critic simply labels the generated features as in-domain or not, without considering the boundaries between classes. This can lead to ambiguous features being generated near class boundaries, reducing target classification accuracy. We propose a novel approach, Adversarial Dropout Regularization (ADR), to encourage the generator to output more discriminative features for the target domain. Our key idea is to replace the critic with one that detects non-discriminative features, using dropout on the classifier network. The generator then learns to avoid these areas of the feature space and thus creates better features. We apply our ADR approach to the problem of unsupervised domain adaptation for image classification and semantic segmentation tasks, and demonstrate significant improvement over the state of the art. We also show that our approach can be used to train Generative Adversarial Networks for semi-supervised learning. We propose a novel method called deep convolutional decision jungle (CDJ) and its learning algorithm for image classification. The CDJ maintains the structure of standard convolutional neural networks (CNNs), i.e. multiple layers of multiple response maps fully connected. Each response map-or node-in both the convolutional and fully-connected layers selectively respond to class labels s.t. each data sample travels via a specific soft route of those activated nodes. The proposed method CDJ automatically learns features, whereas decision forests and jungles require pre-defined feature sets. Compared to CNNs, the method embeds the benefits of using data-dependent discriminative functions, which better handles multi-modal heterogeneous data; further,the method offers more diverse sparse network responses, which in turn can be used for cost-effective learning classification. The network is learnt by combining conventional softmax and proposed entropy losses in each layer. The entropy loss,as used in decision tree growing, measures the purity of data activation according to the class label distribution. The back-propagation rule for the proposed loss function is derived from stochastic gradient descent (SGD) optimization of CNNs. We show that our proposed method outperforms state-of-the-art methods on three public image classification benchmarks and one face verification dataset. We also demonstrate the use of auxiliary data labels, when available, which helps our method to learn more discriminative routing and representations and leads to improved classification. We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the feature space for some standard textural features extracted from the input dataset and then use the theory of Vapnik-Chervonenkis dimension to show that hand-crafted feature extraction creates low-dimensional representations which help in reducing the overall excess error rate. As a corollary to this analysis, we derive for the first time upper bounds on the VC dimension of Convolutional Neural Network as well as Dropout and Dropconnect networks and the relation between excess error rate of Dropout and Dropconnect networks. The concept of intrinsic dimension is used to validate the intuition that texture-based datasets are inherently higher dimensional as compared to handwritten digits or other object recognition datasets and hence more difficult to be shattered by neural networks. We then derive the mean distance from the centroid to the nearest and farthest sampling points in an n-dimensional manifold and show that the Relative Contrast of the sample data vanishes as dimensionality of the underlying vector space tends to infinity. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. Deep convolutional networks have achieved successful performance in data mining field. However, training large networks still remains a challenge, as the training data may be insufficient and the model can easily get overfitted. Hence the training process is usually combined with a model regularization. Typical regularizers include weight decay, Dropout, etc. In this paper, we propose a novel regularizer, named Structured Decorrelation Constraint (SDC), which is applied to the activations of the hidden layers to prevent overfitting and achieve better generalization. SDC impels the network to learn structured representations by grouping the hidden units and encouraging the units within the same group to have strong connections during the training procedure. Meanwhile, it forces the units in different groups to learn non-redundant representations by minimizing the cross-covariance between them. Compared with Dropout, SDC reduces the co-adaptions between the hidden units in an explicit way. Besides, we propose a novel approach called Reg-Conv that can help SDC to regularize the complex convolutional layers. Experiments on extensive datasets show that SDC significantly reduces overfitting and yields very meaningful improvements on classification performance (on CIFAR-10 6.22 accuracy promotion and on CIFAR-100 9.63 promotion). Deep neural networks trained using a softmax layer at the top and the cross-entropy loss are ubiquitous tools for image classification. Yet, this does not naturally enforce intra-class similarity nor inter-class margin of the learned deep representations. To simultaneously achieve these two goals, different solutions have been proposed in the literature, such as the pairwise or triplet losses. However, these carry the extra task of selecting pairs or triplets, and the extra computational burden of computing and learning for many combinations of them. In this paper, we propose a plug-and-play loss term for deep networks that explicitly reduces intra-class variance and enforces inter-class margin simultaneously, in a simple and elegant geometric manner. For each class, the deep features are collapsed into a learned linear subspace, or union of them, and inter-class subspaces are pushed to be as orthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OLA‰) does not require carefully crafting pairs or triplets of samples for training, and works standalone as a classification loss, being the first reported deep metric learning framework of its kind. Because of the improved margin between features of different classes, the resulting deep networks generalize better, are more discriminative, and more robust. We demonstrate improved classification performance in general object recognition, plugging the proposed loss term into existing off-the-shelf architectures. In particular, we show the advantage of the proposed loss in the small data model scenario, and we significantly advance the state-of-the-art on the Stanford STL-10 benchmark. Feedforward multilayer networks trained by supervised learning have recently demonstrated state of the art performance on image labeling problems such as boundary prediction and scene parsing. As even very low error rates can limit practical usage of such systems, methods that perform closer to human accuracy remain desirable. In this work, we propose a new type of network with the following properties that address what we hypothesize to be limiting aspects of existing methods: (1) a wide' structure with thousands of features, (2) a large field of view, (3) recursive iterations that exploit statistical dependencies in label space, and (4) a parallelizable architecture that can be trained in a fraction of the time compared to benchmark multilayer convolutional networks. For the specific image labeling problem of boundary prediction, we also introduce a novel example weighting algorithm that improves segmentation accuracy. Experiments in the challenging domain of connectomic reconstruction of neural circuity from 3d electron microscopy data show that these "Deep And Wide Multiscale Recursive" (DAWMR) networks lead to new levels of image labeling performance. The highest performing architecture has twelve layers, interwoven supervised and unsupervised stages, and uses an input field of view of 157,464 voxels ( @math ) to make a prediction at each image location. We present an associated open source software package that enables the simple and flexible creation of DAWMR networks. We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm). When training a deep neural network for supervised image classification, one can broadly distinguish between two types of latent features of images that will drive the classification of class Y. Following the notation of (2016), we can divide features broadly into the classes of (i) “core” or “conditionally invariant” features X^ci whose distribution P(X^ci | Y) does not change substantially across domains and (ii) “style” or “orthogonal” features X^orth whose distribution P(X^orth | Y) can change substantially across domains. These latter orthogonal features would generally include features such as position, rotation, image quality or brightness but also more complex ones like hair color or posture for images of persons. We try to guard against future adversarial domain shifts by ideally just using the “conditionally invariant” features for classification. In contrast to previous work, we assume that the domain itself is not observed and hence a latent variable. We can hence not directly see the distributional change of features across different domains. We do assume, however, that we can sometimes observe a so-called identifier or ID variable. We might know, for example, that two images show the same person, with ID referring to the identity of the person. In data augmentation, we generate several images from the same original image, with ID referring to the relevant original image. The method requires only a small fraction of images to have an ID variable. We provide a causal framework for the problem by adding the ID variable to the model of (2016). However, we are interested in settings where we cannot observe the domain directly and we treat domain as a latent variable. If two or more samples share the same class and identifier, (Y, ID)=(y,i), then we treat those samples as counterfactuals under different style interventions on the orthogonal or style features. Using this grouping-by-ID approach, we regularize the network to provide near constant output across samples that share the same ID by penalizing with an appropriate graph Laplacian. This is shown to substantially improve performance in settings where domains change in terms of image quality, brightness, color changes, and more complex changes such as changes in movement and posture. We show links to questions of interpretability, fairness and transfer learning. Regularization is key for deep learning since it allows training more complex models while keeping lower levels of overfitting. However, the most prevalent regularizations do not leverage all the capacity of the models since they rely on reducing the effective number of parameters. Feature decorrelation is an alternative for using the full capacity of the models but the overfitting reduction margins are too narrow given the overhead it introduces. In this paper, we show that regularizing negatively correlated features is an obstacle for effective decorrelation and present OrthoReg, a novel regularization technique that locally enforces feature orthogonality. As a result, imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing the regularizer to reach higher decorrelation bounds, and reducing the overfitting more effectively. In particular, we show that the models regularized with OrthoReg have higher accuracy bounds even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of state-of-the-art CNNs on CIFAR-10, CIFAR-100, and SVHN. Regularization is key for deep learning since it allows training more complex models while keeping lower levels of overfitting. However, the most prevalent regularizations do not leverage all the capacity of the models since they rely on reducing the effective number of parameters. Feature decorrelation is an alternative for using the full capacity of the models but the overfitting reduction margins are too narrow given the overhead it introduces. In this paper, we show that regularizing negatively correlated features is an obstacle for effective decorrelation and present OrthoReg, a novel regularization technique that locally enforces feature orthogonality. As a result, imposing locality constraints in feature decorrelation removes interferences between negatively correlated feature weights, allowing the regularizer to reach higher decorrelation bounds, and reducing the overfitting more effectively. In particular, we show that the models regularized with OrthoReg have higher accuracy bounds even when batch normalization and dropout are present. Moreover, since our regularization is directly performed on the weights, it is especially suitable for fully convolutional neural networks, where the weight space is constant compared to the feature map space. As a result, we are able to reduce the overfitting of state-of-the-art CNNs on CIFAR-10, CIFAR-100, and SVHN. We explore a new approach to shape recognition based on a virtually infinite family of binary features (queries) of the image data, designed to accommodate prior information about shape invariance and regularity. Each query corresponds to a spatial arrangement of several local topographic codes (or tags), which are in themselves too primitive and common to be informative about shape. All the discriminating power derives from relative angles and distances among the tags. The important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity; semi-invariance, meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering; and stability, since the queries are not based on distinguished points and substructures. No classifier based on the full feature set can be evaluated, and it is impossible to determine a priori which arrangements are informative. Our approach is to select informative features and build tree classifiers at the same time by inductive learning. In effect, each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed. Due to the number and nature of the queries, standard decision tree construction based on a fixed-length feature vector is not feasible. Instead we entertain only a small random sample of queries at each node, constrain their complexity to increase with tree depth, and grow multiple trees. The terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes. An image is classified by sending it down every tree and aggregating the resulting distributions. The method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred L AT E X symbols. Stateof-the-art error rates are achieved on the National Institute of Standards and Technology database of digits. The principal goal of the experiments on L AT E X symbols is to analyze invariance, generalization error and related issues, and a comparison with artificial neural networks methods is presented in this context. In this work, we investigate the use of sparsity-inducing regularizers during training of Convolution Neural Networks (CNNs). These regularizers encourage that fewer connections in the convolution and fully connected layers take non-zero values and in effect result in sparse connectivity between hidden units in the deep network. This in turn reduces the memory and runtime cost involved in deploying the learned CNNs. We show that training with such regularization can still be performed using stochastic gradient descent implying that it can be used easily in existing codebases. Experimental evaluation of our approach on MNIST, CIFAR, and ImageNet datasets shows that our regularizers can result in dramatic reductions in memory requirements. For instance, when applied on AlexNet, our method can reduce the memory consumption by a factor of four with minimal loss in accuracy. Recent innovations in training deep convolutional neural network (ConvNet) models have motivated the design of new methods to automatically learn local image descriptors. The latest deep ConvNets proposed for this task consist of a siamese network that is trained by penalising misclassification of pairs of local image patches. Current results from machine learning show that replacing this siamese by a triplet network can improve the classification accuracy in several problems, but this has yet to be demonstrated for local image descriptor learning. Moreover, current siamese and triplet networks have been trained with stochastic gradient descent that computes the gradient from individual pairs or triplets of local image patches, which can make them prone to overfitting. In this paper, we first propose the use of triplet networks for the problem of local image descriptor learning. Furthermore, we also propose the use of a global loss that minimises the overall classification error in the training set, which can improve the generalisation capability of the model. Using the UBC benchmark dataset for comparing local image descriptors, we show that the triplet network produces a more accurate embedding than the siamese network in terms of the UBC dataset errors. Moreover, we also demonstrate that a combination of the triplet and global losses produces the best embedding in the field, using this triplet network. Finally, we also show that the use of the central-surround siamese network trained with the global loss produces the best result of the field on the UBC dataset. Pre-trained models are available online at this https URL In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that it's possible to certify the coverage of a coordinate-free sensor network even with very minimal knowledge of the space to be covered. Here, coverage means that every point in the domain (except possibly those very near the boundary) has a nearby sensor. More generally, their algorithm takes a pair of nested neighborhood graphs along with a labeling of vertices as either boundary or interior and computes the relative homology of a simplicial complex induced by the graphs. This approach, called the Topological Coverage Criterion (TCC), requires some assumptions about the underlying geometric domain as well as some assumptions about the relationship of the input graphs to the domain. The goal of this paper is to generalize these assumptions and show how the TCC can be applied to both much more general domains as well as very weak assumptions on the input. We give a new, simpler proof of the de Silva-Ghrist Topological Coverage Criterion that eliminates any assumptions about the smoothness of the boundary of the underlying space, allowing the results to be applied to much more general problems. The new proof factors the geometric, topological, and combinatorial aspects, allowing us to provide a coverage condition that supports thick boundaries, k-coverage, and weighted coverage, in which sensors have varying radii. This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic cyclic, directed undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results. Despite the steady progress in video analysis led by the adoption of convolutional neural networks (CNNs), the relative improvement has been less drastic as that in 2D static image classification. Three main challenges exist including spatial (image) feature representation, temporal information representation, and model computation complexity. It was recently shown by Carreira and Zisserman that 3D CNNs, inflated from 2D networks and pretrained on ImageNet, could be a promising way for spatial and temporal representation learning. However, as for model computation complexity, 3D CNNs are much more expensive than 2D CNNs and prone to overfit. We seek a balance between speed and accuracy by building an effective and efficient video classification system through systematic exploration of critical network design choices. In particular, we show that it is possible to replace many of the 3D convolutions by low-cost 2D convolutions. Rather surprisingly, best result (in both speed and accuracy) is achieved when replacing the 3D convolutions at the bottom of the network, suggesting that temporal representation learning on high-level “semantic” features is more useful. Our conclusion generalizes to datasets with very different properties. When combined with several other cost-effective designs including separable spatial temporal convolution and feature gating, our system results in an effective video classification system that that produces very competitive results on several action classification benchmarks (Kinetics, Something-something, UCF101 and HMDB), as well as two action detection (localization) benchmarks (JHMDB and UCF101-24). Deep convolution neural networks (CNNs) have demonstrated advanced performance on single-label image classification, and various progress also has been made to apply CNN methods on multilabel image classification, which requires annotating objects, attributes, scene categories, etc., in a single shot. Recent state-of-the-art approaches to the multilabel image classification exploit the label dependencies in an image, at the global level, largely improving the labeling capacity. However, predicting small objects and visual concepts is still challenging due to the limited discrimination of the global visual features. In this paper, we propose a regional latent semantic dependencies model (RLSD) to address this problem. The utilized model includes a fully convolutional localization architecture to localize the regions that may contain multiple highly dependent labels. The localized regions are further sent to the recurrent neural networks to characterize the latent semantic dependencies at the regional level. Experimental results on several benchmark datasets show that our proposed model achieves the best performance compared to the state-of-the-art models, especially for predicting small objects occurring in the images. Also, we set up an upper bound model (RLSD+ft-RPN) using bounding-box coordinates during training, and the experimental results also show that our RLSD can approach the upper bound without using the bounding-box annotations, which is more realistic in the real world.