A Tensor-Variate Gaussian Process for Classification of Multidimensional Structured Data
A Tensor-Variate Gaussian Process for Classification of Multidimensional Structured Data
复制标题
DOI：
10.1609/aaai.v27i1.8568
复制
发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Qibin Zhao;Liqing Zhang;A. Cichocki
中科院分区：
文献类型：
--
作者：
Qibin Zhao;Liqing Zhang;A. Cichocki
由于张量提供了多维结构化数据的自然和有效的表示，在本文中，我们考虑概率多项式概率单位分类的张量变量输入高斯过程（GP）的先验放置在潜在的功能。为了考虑到模型中潜在的多模态结构信息，我们提出了一个框架的概率产品核张量数据的基础上生成模型的假设。更具体地说，它可以被解释为映射张量的概率密度函数空间和测量相似性的信息分歧。由于张量核使我们能够对输入张量观测进行建模，因此建议的张量变量GP被认为是生成和判别模型。此外，一个完全变分贝叶斯处理多类GP分类与多项式概率似然估计超参数和推断的预测分布。合成数据和视频中人体动作识别的真实的应用的仿真结果表明，所提出的方法用于多路张量数据分类的有效性和优势，特别是在多模式之间的底层结构信息具有区分性的情况下。分类任务。
As tensors provide a natural and efficient representation of multidimensional structured data, in this paper, we consider probabilistic multinomial probit classification for tensor-variate inputs with Gaussian processes (GP) priors placed over the latent function. In order to take into account the underlying multimodes structure information within the model, we propose a framework of probabilistic product kernels for tensorial data based on a generative model assumption. More specifically, it can be interpreted as mapping tensors to probability density function space and measuring similarity by an information divergence. Since tensor kernels enable us to model input tensor observations, the proposed tensor-variate GP is considered as both a generative and discriminative model. Furthermore, a fully variational Bayesian treatment for multiclass GP classification with multinomial probit likelihood is employed to estimate the hyperparameters and infer the predictive distributions. Simulation results on both synthetic data and a real world application of human action recognition in videos demonstrate the effectiveness and advantages of the proposed approach for classification of multiway tensor data, especially in the case that the underlying structure information among multimodes is discriminative for the classification task.