Coresets vs clustering: comparison of methods for redundancy reduction in very large white matter fiber sets

Alexandroni, Guy; Moreno, Gali Zimmerman; Sochen, Nir; Greenspan, Hayit

doi:10.1117/12.2216461

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Later, coresets were designed for obtaining the first PTAS/LTAS (polynomial/linear time approximation schemes) for more classic and graph problems in theoretical computer science [8][9][10][11]. More recently, coresets appear in machine learning conferences [12][13][14][15][16][17][18][19][20][21] with robotics [12,13,15,16,18,[20][21][22][23][24] and image [25][26][27] applications.…”

Section: Introductionmentioning

confidence: 99%

Autonomous Toy Drone via Coresets for Pose Estimation

Nasser

Jubran

Feldman

2020

Sensors

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A coreset of a dataset is a small weighted set, such that querying the coreset provably yields a ( 1 + ε )-factor approximation to the original (full) dataset, for a given family of queries. This paper suggests accurate coresets ( ε = 0 ) that are subsets of the input for fundamental optimization problems. These coresets enabled us to implement a “Guardian Angel” system that computes pose-estimation in a rate > 20 frames per second. It tracks a toy quadcopter which guides guests in a supermarket, hospital, mall, airport, and so on. We prove that any set of n matrices in R d × d whose sum is a matrix S of rank r, has a coreset whose sum has the same left and right singular vectors as S, and consists of O ( d r ) = O ( d 2 ) matrices, independent of n. This implies the first (exact, weighted subset) coreset of O ( d 2 ) points to problems such as linear regression, PCA/SVD, and Wahba’s problem, with corresponding streaming, dynamic, and distributed versions. Our main tool is a novel usage of the Caratheodory Theorem for coresets, an algorithm that computes its set in time that is linear in its cardinality. Extensive experimental results on both synthetic and real data, companion video of our system, and open code are provided.

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Section: Introductionmentioning

confidence: 99%

Autonomous Toy Drone via Coresets for Pose Estimation

Nasser

Jubran

Feldman

2020

Sensors

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“…Gori et al, 2016, proposed a weighted prototype scheme for fiber bundles in which several ‘prototype’ fibers are chosen among the streamlines to represent groups of similar streamlines. Alexandroni et al, 2016, compared hierarchical clustering methods with different distance metrics to the Coresets approach (Agarwal et al, 2005), and showed the superiority of the latter in fiber set reduction. The underlying goal of all these methods is data compression – they aim to eliminate redundancies and find the set of representative fibers of a bundle.…”

Section: Introductionmentioning

confidence: 99%

Framework for shape analysis of white matter fiber bundles

et al. 2018

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Diffusion imaging coupled with tractography algorithms allows researchers to image human white matter fiber bundles in-vivo. These bundles are three-dimensional structures with shapes that change over time during the course of development as well as in pathologic states. While most studies on white matter variability focus on analysis of tissue properties estimated from the diffusion data, e.g. fractional anisotropy, the shape variability of white matter fiber bundle is much less explored. In this paper, we present a set of tools for shape analysis of white matter fiber bundles, namely: (1) a concise geometric model of bundle shapes; (2) a method for bundle registration between subjects; (3) a method for deformation estimation. Our framework is useful for analysis of shape variability in white matter fiber bundles. We demonstrate our framework by applying our methods on two datasets: one consisting of data for 6 normal adults and another consisting of data for 38 normal children of age 11 days to 8.5 years. We suggest a robust and reproducible method to measure changes in the shape of white matter fiber bundles. We demonstrate how this method can be used to create a model to assess age-dependent changes in the shape of specific fiber bundles. We derive such models for an ensemble of white matter fiber bundles on our pediatric dataset and show that our results agree with normative human head and brain growth data. Creating these models for a large pediatric longitudinal dataset may improve understanding of both normal development and pathologic states and propose novel parameters for the examination of the pediatric brain.

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“…More recently, coresets appear in machine learning conferences Feldman et al (2016bFeldman et al ( , 2011; Tsang et al (2005); Lucic et al (2016); Bachem et al (2016); Lucic et al (2015); Bachem et al (2015); Huggins et al (2016); Rosman et al (2014); Reddi et al (2015). with robotics Feldman et al (2016b); Sung et al (2012); Feldman et al (2013bFeldman et al ( , 2016a; Rosman et al (2014); Feldman et al (2011); Bachem et al (2015); Lucic et al (2016); Bachem et al (2016); Reddi et al (2015) and image Feigin et al (2011); Feldman et al (2013a); Alexandroni et al (2016) applications.…”

Section: Introductionmentioning

confidence: 99%

Coresets for Kinematic Data: From Theorems to Real-Time Systems

Nasser¹,

Jubran²,

Feldman³

2015

Preprint

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A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade, coresets provided breakthroughs in theoretical computer science for approximation algorithms, and more recently, in the machine learning community for learning "Big data". However, we are not aware of real-time systems that compute coresets in a rate of dozens of frames per second. In this paper we suggest a framework to turn theorems to such systems using coresets. We begin with a proof of independent interest, that any set of n matrices in R d×d whose sum is S, has a positively weighted subset whose sum has the same center of mass (mean) and orientation (left+right singular vectors) as S, and consists of O(dr) matrices (independent of n), where r ≤ d is the rank of S. We provide an algorithm that computes this (core) set in one pass over possibly infinite stream of matrices in d O(1) time per matrix insertion. By maintaining such a coreset for kinematic (moving) set of n points, we can run pose-estimation algorithms, such as Kabsch or PnP, on the small coresets, instead of the n points, in real-time using weak devices, while obtaining the same results. This enabled us to implement a low-cost (< $100) IoT wireless system that tracks a toy (and harmless) quadcopter which guides guests to a desired room (in a hospital, mall, hotel, museum, etc.) with no help of additional human or remote controller. See the supp. material for a video that demonstrates our tracking system, including this "Guardian Angel" application. We hope that our framework will encourage researchers outside the theoretical community to design and use coresets in future systems and papers. To this end, we provide extensive experimental results on both synthetic and real data, as well as a link to the open code of our system and algorithms.

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Coresets vs clustering: comparison of methods for redundancy reduction in very large white matter fiber sets

Cited by 4 publications

References 14 publications

Autonomous Toy Drone via Coresets for Pose Estimation

Autonomous Toy Drone via Coresets for Pose Estimation

Framework for shape analysis of white matter fiber bundles

Coresets for Kinematic Data: From Theorems to Real-Time Systems

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