This paper mainly addresses the statistical classification robust to small training data size. We develop a label constrained convolutional factor analysis (LCCFA) model, which unifies the factor analysis (FA), convolution operation and supervised learning. In the LCCFA model, each dictionary atom is used as a small-sized convolution kernel with the goal of learning the observations’ basic structures, which have highly shared characteristics among all observed data. This property enables the proposed method to describe data with fewer dictionary atoms than the FA model and reduces the model complexity. Consequently, the classification performance of the LCCFA model can be improved in the case of limited training samples. Meanwhile, the proposed model also projects the weight vectors of dictionary atoms to their class labels to constrain the learning of parameters. The difference in weight vectors from different classes increases due to the label constraint, thereby offering the potential to enhance the inter-class separability of statistical models. Additionally, the efficient parameter estimation is implemented via variational Bayesian (VB) algorithm. Experimental results on several benchmark datasets and measured radar high-resolution range profile (HRRP) data show that our method outperforms other related models in terms of small sample classification.

本文主要针对小训练数据量的鲁棒统计分类。我们开发了标签约束卷积因子分析（LCCFA）模型，该模型将因子分析（FA），卷积运算和监督学习进行了统一。在LCCFA模型中，每个字典原子都用作小型卷积核，其目的是学习观测的基本结构，该结构在所有观测数据之间具有高度共享的特征。此属性使所提出的方法能够以比FA模型更少的字典原子来描述数据，并降低了模型的复杂性。因此，在训练样本有限的情况下，可以提高LCCFA模型的分类性能。与此同时，该模型还将字典原子的权重向量投影到其类别标签上，以限制参数的学习。来自不同类别的权重向量之间的差异由于标签约束而增加，从而提供了增强统计模型的类别间可分离性的潜力。另外，有效的参数估计是通过变分贝叶斯（VB）算法实现的。在几个基准数据集和测得的雷达高分辨率距离剖面（HRRP）数据上的实验结果表明，在小样本分类方面，我们的方法优于其他相关模型。有效参数估计是通过变分贝叶斯（VB）算法实现的。在几个基准数据集和测得的雷达高分辨率距离剖面（HRRP）数据上的实验结果表明，在小样本分类方面，我们的方法优于其他相关模型。有效参数估计是通过变分贝叶斯（VB）算法实现的。在几个基准数据集和测得的雷达高分辨率距离剖面（HRRP）数据上的实验结果表明，在小样本分类方面，我们的方法优于其他相关模型。