Abstract
Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a multi-dimensional or tensorial format, with each dimension or tensor mode representing different features such as the spatial and temporal information in video sequences or the spatial and spectral information in hyperspectral images. However, in existing compressive learning frameworks, the compressive sensing component utilizes either random or learned linear projection on the vectorized signal to perform signal acquisition, thus discarding the multi-dimensional structure of the signals. In this paper, we propose Multilinear Compressive Learning, a framework that takes into account the tensorial nature of multi-dimensional signals in the acquisition step and builds the subsequent inference model on the structurally sensed measurements. Our theoretical complexity analysis shows that the proposed framework is more efficient compared to its vector-based counterpart in both memory and computation requirement. With extensive experiments, we also empirically show that our Multilinear Compressive Learning framework outperforms the vector-based framework in object classification and face recognition tasks, and scales favorably when the dimensionalities of the original signals increase, making it highly efficient for high-dimensional multi-dimensional signals.
Abstract (translated)
压缩学习是一个新兴的课题,它将通过压缩传感的信号采集和机器学习相结合,直接在少量测量上执行推理任务。许多数据模式自然具有多维或张量格式,每个维度或张量模式代表不同的特征,如视频序列中的时空信息或高光谱图像中的空间和光谱信息。然而,在现有的压缩学习框架中,压缩感测元件利用矢量化信号上的随机或学习线性投影来进行信号采集,从而抛弃了信号的多维结构。本文提出了一种多线性压缩学习框架,该框架考虑了采集过程中多维信号的张量性质,并在结构传感测量的基础上建立了后续的推理模型。我们的理论复杂性分析表明,与基于向量的框架相比,该框架在内存和计算需求方面更为有效。通过大量的实验,我们也从经验上证明了我们的多线性压缩学习框架在目标分类和人脸识别任务上优于基于矢量的学习框架,并且当原始信号的维数增加时,能够很好地扩展,使其对于高维多维信号的处理效率更高。LS
URL
https://arxiv.org/abs/1905.07481