Nauman Shahid

Fast Robust PCA on Graphs

Mining useful clusters from high dimensional data have received significant attention of the computer vision and pattern recognition community in the recent years. Linear and nonlinear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), nonconvexity (for matrix factorization methods), and susceptibility to gross corruptions in the data. In this paper, we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient, and scalable for huge datasets with O(n log(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data.

Locating Temporal Functional Dynamics of Visual Short-Term Memory Binding using Graph Modular Dirichlet Energy

Visual short-term memory binding tasks are a promising early biomarker for Alzheimers disease (AD). We probe the transient physiological underpinnings of these tasks over the healthy brains functional connectome by contrasting shape only (Shape) and shape-colour binding (Bind) conditions, displayed in the left and right sides of the screen, separately, in young volunteers. Electroencephalogram recordings during the encoding and maintenance periods of these tasks are analysed using functional connectomics. Particularly, we introduce and implement a novel technique named Modular Dirichlet Energy (MDE) which allows robust and flexible analysis of the connectome with unprecedentedly high temporal precision. We find that connectivity in the Bind condition is stronger than in the Shape condition in both occipital and frontal network modules during the encoding period of the right screen condition but not the left screen condition. Using MDE we are able to discern driving effects in the occipital module between 100-140ms, which noticeably coincides with the P100 visually evoked potential, and a driving effect in the interaction of occipital and frontal modules between 120-140ms, suggesting a delayed information processing difference between these modules. This provides temporally precise information over a heterogenous population for tasks related to the sensitive and specific detection of AD.Visual short-term memory binding tasks are a promising early marker for Alzheimer’s disease (AD). To uncover functional deficits of AD in these tasks it is meaningful to first study unimpaired brain function. Electroencephalogram recordings were obtained from encoding and maintenance periods of tasks performed by healthy young volunteers. We probe the task’s transient physiological underpinnings by contrasting shape only (Shape) and shape-colour binding (Bind) conditions, displayed in the left and right sides of the screen, separately. Particularly, we introduce and implement a novel technique named Modular Dirichlet Energy (MDE) which allows robust and flexible analysis of the functional network with unprecedented temporal precision. We find that connectivity in the Bind condition is less integrated with the global network than in the Shape condition in occipital and frontal modules during the encoding period of the right screen condition. Using MDE we are able to discern driving effects in the occipital module between 100–140 ms, coinciding with the P100 visually evoked potential, followed by a driving effect in the frontal module between 140–180 ms, suggesting that the differences found constitute an information processing difference between these modules. This provides temporally precise information over a heterogeneous population in promising tasks for the detection of AD.

Graph-based sinogram denoising for tomographic reconstructions

Limited data and low-dose constraints are common problems in a variety of tomographic reconstruction paradigms, leading to noisy and incomplete data. Over the past few years, sinogram denoising has become an essential preprocessing step for low-dose Computed Tomographic (CT) reconstructions. We propose a novel sinogram denoising algorithm inspired by signal processing on graphs. Graph-based methods often perform better than standard filtering operations since they can exploit the signal structure. This makes the sinogram an ideal candidate for graph based denoising since it generally has a piecewise smooth structure. We test our method with a variety of phantoms using different reconstruction methods. Our numerical study shows that the proposed algorithm improves the performance of analytical filtered back-projection (FBP) and iterative methods such as ART (Kaczmarz), and SIRT (Cimmino). We observed that graph denoised sinograms always minimize the error measure and improve the accuracy of the solution, compared to regular reconstructions.

PCA using graph total variation

Mining useful clusters from high dimensional data has received significant attention of the signal processing and machine learning community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with problems such as high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) or susceptibility to gross corruptions in the data. In this paper we propose a convex, robust, scalable and efficient Principal Component Analysis (PCA) based method to approximate the low-rank representation of high dimensional datasets via a two-way graph regularization scheme. Compared to the exact recovery methods, our method is approximate, in that it enforces a piecewise constant assumption on the samples using a graph total variation and a piecewise smoothness assumption on the features using a graph Tikhonov regularization. Futhermore, it retrieves the low-rank representation in a time that is linear in the number of data samples. Clustering experiments on 3 benchmark datasets with different types of corruptions show that our proposed model outperforms 7 state-of-the-art dimensionality reduction models.

SVM Based Event Detection and Identification: Exploiting Temporal Attribute Correlations Using SensGru

In the context of anomaly detection in cyber physical systems (CPS), spatiotemporal correlations are crucial for high detection rate. This work presents a new quarter sphere support vector machine (QS-SVM) formulation based on the novel concept of attribute correlations. Our event detection approach, SensGru, groups multiple sensors on a single node and thus eliminates communication between sensor nodes without compromising the advantages of spatial correlation. It makes use of temporal-attribute (TA) correlations and is thus a TA-QS-SVM formulation. We show analytically that SensGru (or interchangeably TA-QS-SVM) results in a reduced node density and gives the same event detection performance as more dense Spatiotemporal-Attribute Quarter-Sphere SVM (STA-QS-SVM) formulation which exploits both spatiotemporal and attribute correlations. Moreover, this paper develops theoretical bounds on the internode distance, the optimal number of sensors, and the sensing range with SensGru so that the performance difference with SensGru and STA-QS-SVM is negligibly small. Both schemes achieve event detection rates as high as 100% and an extremely low false positive rate.