Mining useful clusters from high dimensional data has received significant
attention of the computer vision and pattern recognition 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 three different problems: high computational
complexity (usually associated with the nuclear norm minimization),
non-convexity (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(nlog(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
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called 'Robust PCA on Graphs' which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks.
Machine learning, like its various applications, has received a great interest in outlier detection in Wireless Sensor Networks. Support Vector Machines (SVM) are a special type of Machine learning techniques which are computationally inexpensive and provide a sparse solution. This work presents a detailed analysis of various formulations of one-class SVMs, like, hyper-plane, hyper-sphere, quarter-sphere and hyper-ellipsoidal. These formulations are used to separate the normal data from anomalous data. Various techniques based on these formulations have been analyzed in terms of a number of characteristics for harsh environments. These characteristics include input data type, spatio-temporal and attribute correlations, user specified thresholds, outlier types, outlier identification(event/error), outlier degree, susceptibility to dynamic topology, non-stationarity and inhomogeneity. A tabular description of improvement and feasibility of various techniques for deployment in the harsh environments has also been presented.
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.
Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional artifacts due to over-smoothing. Non-Local TV (NLTV) methods have been proposed as a solution to this but they either lack continuous updates due to computational constraints or limit the locality to a small region. In this paper we propose Adaptive Graph-based TV (AGTV). The proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the entire image regardless of spatial distance. As compared to NLTV the proposed method is computationally efficient and involves updating the graph prior during every iteration making the connection between similar regions stronger. Moreover, it promotes sparsity in the wavelet and graph gradient domains. Since TV is a special case of graph TV the proposed method can also be seen as a generalization of SER and TV methods.
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