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- Alexander Cloninger, Wojciech Czaja, Ruiliang Bai, Peter J. Basser
- SIAM J. Imaging Sciences
- 2014

We present an algorithm to solve the two-dimensional Fredholm integral of the first kind with tensor product structure from a limited number of measurements, with the goal of using this method to speed up nuclear magnetic resonance spectroscopy. This is done by incorporating compressive sensing–type arguments to fill in missing measurements, using a priori… (More)

- Uri Shaham, Alexander Cloninger, Ronald R. Coifman
- ArXiv
- 2015

We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ ⊂ R m , we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and… (More)

- Gal Mishne, Uri Shaham, Alexander Cloninger, Israel Cohen
- ArXiv
- 2015

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded… (More)

- Ruiliang Bai, Alexander Cloninger, Wojciech Czaja, Peter J Basser
- Journal of magnetic resonance
- 2015

Potential applications of 2D relaxation spectrum NMR and MRI to characterize complex water dynamics (e.g., compartmental exchange) in biology and other disciplines have increased in recent years. However, the large amount of data and long MR acquisition times required for conventional 2D MR relaxometry limits its applicability for in vivo preclinical and… (More)

- Alexander Cloninger, Wojciech Czaja, Timothy Doster
- IGARSS
- 2014

As new sensing modalities emerge and the presence of multiple sensors per platform becomes widespread, it is vital to develop new algorithms and techniques which can fuse this data. Many of previous attempts to deal with the problem of heterogeneous data integration for the applications in data classification were either highly data dependent or relied on… (More)

- Ariel Hafftka, Hasan Celik, Alexander Cloninger, Wojciech Czaja, Richard G. Spencer
- 2015 International Conference on Sampling Theory…
- 2015

In [1], Cloninger, Czaja, Bai, and Basser developed an algorithm for compressive sampling based data acquisition for the solution of 2D Fredholm equations. We extend the algorithm to N dimensional data, by randomly sampling in 2 dimensions and fully sampling in the remaining N-2 dimensions. This new algorithm has direct applications to 3-dimensional nuclear… (More)

- Alexander Cloninger, Wojciech Czaja
- 2015 International Conference on Sampling Theory…
- 2015

We aim to understand and characterize embeddings of datasets with small anomalous clusters using the Laplacian Eigenmaps algorithm. To do this, we characterize the order in which eigenvectors of a disjoint graph Laplacian emerge and the support of those eigenvectors. We then extend this characterization to weakly connected graphs with clusters of differing… (More)

- Noreen Jamil, Xuemei Chen, Alexander Cloninger
- J. Computational Applied Mathematics
- 2015

The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We apply the Hildreth's algorithm, as well as a randomized version, along with prioritized selection of the inequalities, to… (More)

- Alexander Cloninger
- ArXiv
- 2016

We note that building a magnetic Laplacian from the Markov transition matrix, rather than the graph adjacency matrix, yields several benefits for the magnetic eigenmaps algorithm. The two largest benefits are that the embedding becomes more stable as a function of the rotation parameter g, and the principal eigenvector of the magnetic Laplacian now… (More)

Previous research has shown that neural networks can model survival data in situations in which some patients' death times are unknown, e.g. right-censored. However, neural networks have rarely been shown to outperform their linear counterparts such as the Cox proportional hazards model. In this paper, we run simulated experiments and use real survival data… (More)