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In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal…
The purpose of feature extraction on convolutional neural networks is to reuse deep representations learnt for a pre-trained model to solve a new, potentially unrelated problem. However, raw feature extraction from all layers is unfeasible…
It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the…
One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…
Deep neural networks are representation learning techniques. During training, a deep net is capable of generating a descriptive language of unprecedented size and detail in machine learning. Extracting the descriptive language coded within…
Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…
Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…
Recently, intermediate feature maps of pre-trained convolutional neural networks have shown significant perceptual quality improvements, when they are used in the loss function for training new networks. It is believed that these features…
The Convolutional Neural Networks (CNNs), in domains like computer vision, mostly reduced the need for handcrafted features due to its ability to learn the problem-specific features from the raw input data. However, the selection of…
Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method…
Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…
Shape learning, or the ability to leverage shape information, could be a desirable property of convolutional neural networks (CNNs) when target objects have specific shapes. While some research on the topic is emerging, there is no…
Deep learning, as a promising new area of machine learning, has attracted a rapidly increasing attention in the field of medical imaging. Compared to the conventional machine learning methods, deep learning requires no hand-tuned feature…