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FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
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Cited by 248 (6 self)
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Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing lowrank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed—either explicitly or implicitly—to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired lowrank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, speed, and robustness. These claims are supported by extensive numerical experiments and a detailed error analysis. The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition
Scalable knn graph construction for visual descriptors
 In CVPR
"... The kNN graph has played a central role in increasingly popular datadriven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct kNN graphs remains a challenge, especially for largescale highdimensional data. In this paper, we propose a new ..."
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Cited by 14 (4 self)
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The kNN graph has played a central role in increasingly popular datadriven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct kNN graphs remains a challenge, especially for largescale highdimensional data. In this paper, we propose a new approach to construct approximate kNN graphs with emphasis in: efficiency and accuracy. We hierarchically and randomly divide the data points into subsets and build an exact neighborhood graph over each subset, achieving a base approximate neighborhood graph; we then repeat this process for several times to generate multiple neighborhood graphs, which are combined to yield a more accurate approximate neighborhood graph. Furthermore, we propose a neighborhood propagation scheme to further enhance the accuracy. We show both theoretical and empirical accuracy and efficiency of our approach to kNN graph construction and demonstrate significant speedup in dealing with large scale visual data. 1.
Discovering Hidden Relationships via Efficient Coclustering of Sparse Matrices∗
"... We present a new approach for discovering hidden relationships in sparse bipartite data by identifying large, dense biclusters in the corresponding matrix. We motivate a new class of metrics to measure the quality of a bicluster partition, and compare them to existing metrics. We then present a h ..."
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We present a new approach for discovering hidden relationships in sparse bipartite data by identifying large, dense biclusters in the corresponding matrix. We motivate a new class of metrics to measure the quality of a bicluster partition, and compare them to existing metrics. We then present a heuristic algorithm that efficiently searches the space of possible coclusterings for one which maximizes the value of a given metric. We evaluate our approach with experiments on synthetic and realworld datasets.
ABSTRACT OF THE DISSERTATION Models and Algorithms for EventDriven Networks
, 2014
"... Many realworld systems can be represented as networks driven by discrete events, each event identified by the time at which it occurs and the parties involved. An event could be a meeting, a stock trade, a phone call, an email, a gang fight, an online or offline purchase, a blog post, a conference ..."
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Many realworld systems can be represented as networks driven by discrete events, each event identified by the time at which it occurs and the parties involved. An event could be a meeting, a stock trade, a phone call, an email, a gang fight, an online or offline purchase, a blog post, a conference, or the transmission of an IP packet. Innovations in technology have increased our ability to collect massive amounts of digital data from such networks, which presents both new opportunities and new challenges. In this work, we develop new theoretical models and efficient algorithms that leverage the temporal and relational information inherent in the data to better understand and analyze realworld networks. In particular, we consider three problems: (1) detecting correlated events in communication networks; (2) discovering functional communities; and (3) modeling collaboration in academia. First we present a new stochastic model for eventdriven networks, and with it develop two algorithms – a streaming local algorithm, and an efficient global algorithm – to detect statistically correlated activity. We demonstrate that our approach, which models each communication channel as its own stochastic process, is better able to accommodate the temporal variability present in realworld communication networks than existing methods.
Acknowledgements
, 2015
"... Student, Sami Sieranoja: High dimensional k nearest neighbor graph construc ..."
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Student, Sami Sieranoja: High dimensional k nearest neighbor graph construc
Rotationally Invariant Image Representation for Viewing Direction Classification in CryoEM
"... We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of CryoEM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compres ..."
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We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of CryoEM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than referencefree alignment with rotationally invariant Kmeans clustering and MSA/MRA 2D classification.
Article Using Visible Spectral Information to Predict LongWave Infrared Spectral Emissivity: A Case Study over the Sokolov Area of the Czech Republic with an Airborne Hyperspectral Scanner Sensor
, 2013
"... Abstract: Remotesensing platforms are often comprised of a cluster of different spectral range detectors or sensors to benefit from the spectral identification capabilities of each range. Missing data from these platforms, caused by problematic weather conditions, such as clouds, sensor failure, lo ..."
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Abstract: Remotesensing platforms are often comprised of a cluster of different spectral range detectors or sensors to benefit from the spectral identification capabilities of each range. Missing data from these platforms, caused by problematic weather conditions, such as clouds, sensor failure, low temporal coverage or a narrow field of view (FOV), is one of the problems preventing proper monitoring of the Earth. One of the possible solutions is predicting a detector or sensor’s missing data using another detector/sensor. In this paper, we propose a new method of predicting spectral emissivity in the longwave infrared (LWIR) spectral region using the visible (VIS) spectral region. The proposed method is suitable for two main scenarios of missing data: sensor malfunctions and narrow FOV. We demonstrate the usefulness and limitations of this prediction scheme using the airborne hyperspectral scanner (AHS) sensor, which consists of both VIS and LWIR spectral regions, in a case study over the Sokolov area, Czech Republic.
Rotationally Invariant Image Representation for Viewing Direction Classification in CryoEM
"... We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of cryoEM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compres ..."
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We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of cryoEM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than referencefree alignment with rotationally invariant Kmeans clustering, MSA/MRA 2D classification, and their modern approximations.