Neuron matching in C. elegans with robust approximate linear regression without correspondence
Neuron matching in C. elegans with robust approximate linear regression without correspondence
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DOI：
10.1109/wacv48630.2021.00288
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Amin Nejatbakhsh;E. Varol
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文献类型：
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作者：
Amin Nejatbakhsh;E. Varol
我们提出的方法估计两个点集之间的对应关系下存在的离群值在源和目标集。所提出的算法扩展了无对应问题的回归理论，利用协变量和响应的无序多集来估计变换系数。以前的理论分析的问题已经做了设置的反应是一个完整的排列的回归协变量。本文通过分析只有一个子集的响应是一个置换的回归协变量的情况下，除了一些协变量可能是敌对的离群值扩展的问题设置。我们这个问题的鲁棒回归没有对应关系，并提供了几个算法的基础上随机样本的共识，在一个无噪声和嘈杂的一维设置以及多个维度的近似算法的精确和近似恢复。仿真数据验证了算法的理论保证。我们证明了一个重要的计算神经科学的应用所提出的框架，通过证明其有效性秀丽隐杆线虫神经元匹配问题的存在下，在源和目标线虫的离群值是一个自然的趋势。实现此方法的开源代码可在www.example.com上获得。
We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to estimate transformation coefficients using unordered multisets of covariates and responses. Previous theoretical analysis of the problem has been done in a setting where the responses are a complete permutation of the regressed covariates. This paper expands the problem setting by analyzing the cases where only a subset of the responses is a permutation of the regressed covariates in addition to some covariates possibly being adversarial outliers. We term this problem robust regression without correspondence and provide several algorithms based on random sample consensus for exact and approximate recovery in a noiseless and noisy one-dimensional setting as well as an approximation algorithm for multiple dimensions. The theoretical guarantees of the algorithms are verified in simulated data. We demonstrate an important computational neuroscience application of the proposed framework by demonstrating its effectiveness in a Caenorhabditis elegans neuron matching problem where the presence of outliers in both the source and target nematodes is a natural tendency. Open source code implementing this method is available at https://github.com/amin-nejat/RRWOC.