892 research outputs found
Convex relaxation of mixture regression with efficient algorithms
We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Large-Scale Sensor Network Localization via Rigid Subnetwork Registration
In this paper, we describe an algorithm for sensor network localization (SNL)
that proceeds by dividing the whole network into smaller subnetworks, then
localizes them in parallel using some fast and accurate algorithm, and finally
registers the localized subnetworks in a global coordinate system. We
demonstrate that this divide-and-conquer algorithm can be used to leverage
existing high-precision SNL algorithms to large-scale networks, which could
otherwise only be applied to small-to-medium sized networks. The main
contribution of this paper concerns the final registration phase. In
particular, we consider a least-squares formulation of the registration problem
(both with and without anchor constraints) and demonstrate how this otherwise
non-convex problem can be relaxed into a tractable convex program. We provide
some preliminary simulation results for large-scale SNL demonstrating that the
proposed registration algorithm (together with an accurate localization scheme)
offers a good tradeoff between run time and accuracy.Comment: 5 pages, 8 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
Study and Observation of the Variation of Accuracies of KNN, SVM, LMNN, ENN Algorithms on Eleven Different Datasets from UCI Machine Learning Repository
Machine learning qualifies computers to assimilate with data, without being
solely programmed [1, 2]. Machine learning can be classified as supervised and
unsupervised learning. In supervised learning, computers learn an objective
that portrays an input to an output hinged on training input-output pairs [3].
Most efficient and widely used supervised learning algorithms are K-Nearest
Neighbors (KNN), Support Vector Machine (SVM), Large Margin Nearest Neighbor
(LMNN), and Extended Nearest Neighbor (ENN). The main contribution of this
paper is to implement these elegant learning algorithms on eleven different
datasets from the UCI machine learning repository to observe the variation of
accuracies for each of the algorithms on all datasets. Analyzing the accuracy
of the algorithms will give us a brief idea about the relationship of the
machine learning algorithms and the data dimensionality. All the algorithms are
developed in Matlab. Upon such accuracy observation, the comparison can be
built among KNN, SVM, LMNN, and ENN regarding their performances on each
dataset.Comment: To be published in the 4th IEEE International Conference on
Electrical Engineering and Information & Communication Technology (iCEEiCT
2018
Image Partitioning based on Semidefinite Programming
Many tasks in computer vision lead to combinatorial optimization problems. Automatic image partitioning is one of the most important examples in this context: whether based on some prior knowledge or completely unsupervised, we wish to find coherent parts of the image. However, the inherent combinatorial complexity of such problems often prevents to find the global optimum in polynomial time. For this reason, various approaches have been proposed to find good approximative solutions for image partitioning problems. As an important example, we will first consider different spectral relaxation techniques: based on straightforward eigenvector calculations, these methods compute suboptimal solutions in short time. However, the main contribution of this thesis is to introduce a novel optimization technique for discrete image partitioning problems which is based on a semidefinite programming relaxation. In contrast to approximation methods employing annealing algorithms, this approach involves solving a convex optimization problem, which does not suffer from possible local minima. Using interior point techniques, the solution of the relaxation can be found in polynomial time, and without elaborate parameter tuning. High quality solutions to the original combinatorial problem are then obtained with a randomized rounding technique. The only potential drawback of the semidefinite relaxation approach is that the number of variables of the optimization problem is squared. Nevertheless, it can still be applied to problems with up to a few thousand variables, as is demonstrated for various computer vision tasks including unsupervised segmentation, perceptual grouping and image restoration. Concerning problems of higher dimensionality, we study two different approaches to effectively reduce the number of variables. The first one is based on probabilistic sampling: by considering only a small random fraction of the pixels in the image, our semidefinite relaxation method can be applied in an efficient way while maintaining a reliable quality of the resulting segmentations. The second approach reduces the problem size by computing an over-segmentation of the image in a preprocessing step. After that, the image is partitioned based on the resulting "superpixels" instead of the original pixels. Since the real world does not consist of pixels, it can even be argued that this is the more natural image representation. Initially, our semidefinite relaxation method is defined only for binary partitioning problems. To derive image segmentations into multiple parts, one possibility is to apply the binary approach in a hierarchical way. Besides this natural extension, we also discuss how multiclass partitioning problems can be solved in a direct way based on semidefinite relaxation techniques
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