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Showing 1 to 17 of 17 for “"Random projections"”.
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Approximate k-means clustering through random projections
Using random row projections, we show how to approximate a data matrix A with a much smaller sketch à that can be used to solve a general class of constrained k-rank approximation problems to within (1 + [epsilon]) error. Importantly, this class of problems includes k-means clustering. By reducing …
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A Method for Clustering High-Dimensional Data Using 1D Random Projections
… clustering method using a binary tree of 1D random projections. As real data tends to have a lot of structures, we show that a 1D random projection of real data captures some of that structure with a high probability. More specifically, the structure manifests itself as a clear binary …
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Focused polynomials, random projections and approximation algorithms for polynomial optimization over the sphere
… These polynomials can be well approximated by a random projection, reducing the problem to optimization over a sphere of a much smaller dimension. We then introduce polynomials generated from a focused cone, which generalizes focused polynomials, and show that the dimension required for the …
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Informative sensing : theory and applications
… information can be captured faithfully with few random measurement samples, even far below the Nyquist rate. Despite the successful story, we question how the theory would change if we had a more precise prior than the simple sparsity model. Hence, we consider the settings where the prior is …
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Optimization over networks: Efficient algorithms and analysis
… set. We propose gradient descent algorithms with random projections which use various communication protocols. First, we present a distributed random projection (DRP) algorithm whereby each agent exchanges local information only with its immediate neighbors at each iteration. With reasonable …
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Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing
… algorithms, namely the Nystrom extension, Random Projections, and Approximate Neighborhood constructions. The Nystrom extension is studied in detail and the application of Frame Theory and Sigma-Delta Quantization is proposed to enrich the Nystrom extension.
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Generative modeling using the sliced Wasserstein distance
… formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddlepoint formulation. By augmenting this approach with a discriminator we improve its accuracy. We found our approach to be significantly more stable …
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New approaches to modern statistical classification problems
… of applying an arbitrary base classifier on random projections of the feature vectors into a lower-dimensional space. In one special case that we study in detail, the random projections are divided into non-overlapping blocks, and within each block we select the projection yielding the …
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The North Pole Problem and Recent Developments in Infinitesimal Free Probability
… phenomena in the large N limit involving random rotations of the north pole and random projections associated with Haar orthogonal matrices.
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Novel Fast Algorithms For Low Rank Matrix Approximation
… in matrix approximation have seen an emphasis on randomization techniques in which the goal was to create a sketch of an input matrix. This sketch, a random submatrix of an input matrix, having much fewer rows or columns, still preserves its relevant features. In one of such techniques random …
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Low-Density Cluster Separators for Large, High-Dimensional, Mixed and Non-Linearly Separable Data.
… searches over a collection of one-dimensional random projections for an appropriate subspace for cluster identification. The proposed approaches produce high-quality partitions, that are competitive with well-established and state-of-the-art algorithms.
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Random projection methods for stochastic convex minimization
… closed and convex sets. The problem has random features. Gradient or subgradient of objective function carries stochastic errors. Number of constraint sets can be extensive or infinitely many. Constraint sets might not be known apriori yet revealed through random realizations or randomly …
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Visual feature learning with application to medical image classification
… to other descriptors such as root-SIFT and Random Projections. Finally, I propose an approach to improve feature encoding methods. The approach captures inter-cluster features, providing context information in the feature as well as in the image spaces, in addition to the intra-cluster …
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Reduced complexity adaptive beamformers
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms
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New statistical perspectives on efficient Big Data algorithms for high-dimensional Bayesian regression and model selection
… the computer science community. Sketching uses random projection to compress the original large dataset, producing a smaller surrogate dataset that is less computationally demanding to work with. The sketched dataset can be used for approximate inference. We test our regression algorithms on a …
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Restricting Supervised Learning: Feature Selection and Feature Space Partition
… minimum conditional entropy with respect to random projections. This approach was tested on three artificial data sets, three cheminformatics data sets, and two leukemia gene expression data sets. Empirical results demonstrate that our method is capable of selecting a proper discrete or …
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Large-Scale Machine Learning for Classification and Search
… between two data points through Markov random walks. 2. Large-Scale Semi-Supervised Learning: We employ Anchor Graphs to develop a scalable solution for semi-supervised learning, which capitalizes on both labeled and unlabeled data to learn graph-based classification models. We propose …