Simplified Energy Landscape for Modularity Using Total Variation

Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in these applications, and identifying them gives insight into the overall organization of the network. One common quality function used to identify community structure is modularity. In Hu et al. [SIAM J. App. Math., 73(6), 2013], it was shown that modularity optimization is equivalent to minimizing a particular nonconvex total variation (TV) based functional over a discrete domain. They solve this problem, assuming the number of communities is known, using a Merriman, Bence, Osher (MBO) scheme. We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain, again, assuming the number of communities is known. Furthermore, we show that modularity has no convex relaxation satisfying certain natural conditions. We therefore, find a manageable non-convex approximation using a Ginzburg Landau functional, which provably converges to the correct energy in the limit of a certain parameter. We then derive an MBO algorithm with fewer hand-tuned parameters than in Hu et al. and which is 7 times faster at solving the associated diffusion equation due to the fact that the underlying discretization is unconditionally stable. Our numerical tests include a hyperspectral video whose associated graph has 2.9x10^7 edges, which is roughly 37 times larger than was handled in the paper of Hu et al.Comment: 25 pages, 3 figures, 3 tables, submitted to SIAM J. App. Mat

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

On the data hiding theory and multimedia content security applications

This dissertation is a comprehensive study of digital steganography for multimedia content protection. With the increasing development of Internet technology, protection and enforcement of multimedia property rights has become a great concern to multimedia authors and distributors. Watermarking technologies provide a possible solution for this problem. The dissertation first briefly introduces the current watermarking schemes, including their applications in video,, image and audio. Most available embedding schemes are based on direct Spread Sequence (SS) modulation. A small value pseudo random signature sequence is embedded into the host signal and the information is extracted via correlation. The correlation detection problem is discussed at the beginning. It is concluded that the correlator is not optimum in oblivious detection. The Maximum Likelihood detector is derived and some feasible suboptimal detectors are also analyzed. Through the calculation of extraction Bit Error Rate (BER), it is revealed that the SS scheme is not very efficient due to its poor host noise suppression. The watermark domain selection problem is addressed subsequently. Some implications on hiding capacity and reliability are also studied. The last topic in SS modulation scheme is the sequence selection. The relationship between sequence bandwidth and synchronization requirement is detailed in the work. It is demonstrated that the white sequence commonly used in watermarking may not really boost watermark security. To address the host noise suppression problem, the hidden communication is modeled as a general hypothesis testing problem and a set partitioning scheme is proposed. Simulation studies and mathematical analysis confirm that it outperforms the SS schemes in host noise suppression. The proposed scheme demonstrates improvement over the existing embedding schemes. Data hiding in audio signals are explored next. The audio data hiding is believed a more challenging task due to the human sensitivity to audio artifacts and advanced feature of current compression techniques. The human psychoacoustic model and human music understanding are also covered in the work. Then as a typical audio perceptual compression scheme, the popular MP3 compression is visited in some length. Several schemes, amplitude modulation, phase modulation and noise substitution are presented together with some experimental results. As a case study, a music bitstream encryption scheme is proposed. In all these applications, human psychoacoustic model plays a very important role. A more advanced audio analysis model is introduced to reveal implications on music understanding. In the last part, conclusions and future research are presented

Feature Encoding Strategies for Multi-View Image Classification

Machine vision systems can vary greatly in size and complexity depending on the task at hand. However, the purpose of inspection, quality and reliability remains the same. This work sets out to bridge the gap between traditional machine vision and computer vision. By applying powerful computer vision techniques, we are able to achieve more robust solutions in manufacturing settings. This thesis presents a framework for applying powerful new image classification techniques used for image retrieval in the Bag of Words (BoW) framework. In addition, an exhaustive evaluation of commonly used feature pooling approaches is conducted with results showing that spatial augmentation can outperform mean and max descriptor pooling on an in-house dataset and the CalTech 3D dataset. The results for the experiments contained within, details a framework that performs classification using multiple view points. The results show that the feature encoding method known as Triangulation Embedding outperforms the Vector of Locally Aggregated Descriptors (VLAD) and the standard BoW framework with an accuracy of 99.28%. This improvement is also seen on the public Caltech 3D dataset where the improvement over VLAD and BoW was 5.64% and 12.23% respectively. This proposed multiple view classification system is also robust enough to handle the real world problem of camera failure and still classify with a high reliability. A missing camera input was simulated and showed that using the Triangulation Embedding method, the system could perform classification with a very minor reduction in accuracy at 98.89%, compared to the BoW baseline at 96.60% using the same techniques. The presented solution tackles the traditional machine vision problem of object identification and also allows for the training of a machine vision system that can be done without any expert level knowledge

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

A path following algorithm for the graph matching problem

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,

State-space model with deep learning for functional dynamics estimation in resting-state fMRI

Studies on resting-state functional Magnetic Resonance Imaging (rs-fMRI) have shown that different brain regions still actively interact with each other while a subject is at rest, and such functional interaction is not stationary but changes over time. In terms of a large-scale brain network, in this paper, we focus on time-varying patterns of functional networks, i.e., functional dynamics, inherent in rs-fMRI, which is one of the emerging issues along with the network modelling. Specifically, we propose a novel methodological architecture that combines deep learning and state-space modelling, and apply it to rs-fMRI based Mild Cognitive Impairment (MCI) diagnosis. We first devise a Deep Auto-Encoder (DAE) to discover hierarchical non-linear functional relations among regions, by which we transform the regional features into an embedding space, whose bases are complex functional networks. Given the embedded functional features, we then use a Hidden Markov Model (HMM) to estimate dynamic characteristics of functional networks inherent in rs-fMRI via internal states, which are unobservable but can be inferred from observations statistically. By building a generative model with an HMM, we estimate the likelihood of the input features of rs-fMRI as belonging to the corresponding status, i.e., MCI or normal healthy control, based on which we identify the clinical label of a testing subject. In order to validate the effectiveness of the proposed method, we performed experiments on two different datasets and compared with state-of-the-art methods in the literature. We also analyzed the functional networks learned by DAE, estimated the functional connectivities by decoding hidden states in HMM, and investigated the estimated functional connectivities by means of a graph-theoretic approach