NNR-GL: A Measure to Detect Co-Nonlinearity Based on Neural Network Regression Regularized by Group Lasso
NNR-GL: A Measure to Detect Co-Nonlinearity Based on Neural Network Regression Regularized by Group Lasso
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DOI：
10.1109/access.2021.3111105
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发表时间：
2021
期刊：
影响因子：
3.9
通讯作者：
M. Ohsaki;Naoya Kishimoto;Hayato Sasaki;Ryoji Ikeura;S. Katagiri;K. Ohnishi;Yakub Sebastian;P. Then
中科院分区：
文献类型：
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作者：
M. Ohsaki;Naoya Kishimoto;Hayato Sasaki;Ryoji Ikeura;S. Katagiri;K. Ohnishi;Yakub Sebastian;P. Then
为了找到理解和阐明一种现象的关键，检测变量之间的相关性是必不可少的，因此已经提出了相关措施。相关系数及其变体是最常见的，但它们只能检测两个变量之间的线性相关性（共线性）。最近的一些措施可以检测的非线性依赖（共非线性）的核化或分割。他们应该只处理两个变量，并就检测性能和设置难度进行讨论。基于神经网络（NN）的新措施有空间，因为通常的NN的目标是预测，而不是变量相关性检测。为了高性能地检测多个变量之间的协非线性，我们提出了一种基于群套索（GL）正则化神经网络回归（NNR）的称为NNR-GL的度量。NNR-GL体现了NNR通过多输入单输出回归进行检测，GL在输入层进行正则化。然后，NNR-GL通过统一回归性能和输入变量的权重来计算检测到的协非线性的强度。我们使用人工数据进行了实验，以检查NNR-GL的行为和基本有效性。通过综合检测性能标准（简称CDP-AUC）评估性能，该标准是代表真阳性和真阴性检测的曲线下面积的平均值。NNR-GL达到的CDP-AUC值为0.7472 - 0.9681，其中0表示检测完全失败，1表示检测完全成功。这些值始终高于那些从0.5972到0.9259的传统措施的所有不同条件的依赖性，数据大小，和噪声率。因此，明确证实了NNR-GL的有效性和耐用性。
For finding keys to understand and elucidate a phenomenon, it is essential to detect dependences among variables, and so measures for that have been proposed. Correlation coefficient and its variants are most common, but they only detect a linear dependence (co-linearity) between two variables. Some recent measures can detect a nonlinear dependence (co-nonlinearity) by means of kernelization or segmentation. They are supposed to handle two variables only and open to discussion with regard to performance in detection and difficulty in setup. There is room for a novel measure based on Neural Networks (NNs), since usual NNs aim at prediction but not at variable dependence detection. For the high-performance detection of co-nonlinearities among multi variables, we propose a measure called NNR-GL based on Neural Network Regression (NNR) regularized by Group Lasso (GL). NNR-GL embodies the detection through multi-input single-output regression by NNR and regularization on the input layer by GL. NNR-GL then calculates how strong the detected co-nonlinearities are by unifying the regression performance and the weights on input variables. We conducted experiments using artificial data to examine the behaviors and fundamental effectiveness of NNR-GL. The performance was estimated by a comprehensive detection performance criterion (CDP-AUC in short), which is the mean of area under curves representing true positive and true negative detections. NNR-GL achieved the values of CDP-AUC from 0.7472 to 0.9681, where 0 means complete failure and 1 means complete success in detection. These values were consistently higher than those from 0.5972 to 0.9259 of the conventional measures for all the different conditions of dependence, data size, and noise rate. Consequently, the effectiveness and robustness of NNR-GL were clearly confirmed.