Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying latent structure in the data. In this work, we incorporate a generative manifold model into the latent space of an autoencoder in order to learn the low-dimensional manifold structure from the data and adapt the latent space to accommodate this structure. In particular, we focus on applications in which the data has closed transformation paths which extend from a starting point and return to nearly the same point. Through experiments on data with natural closed transformation paths, we show that this model introduces the ability to learn the latent dynamics of complex systems, generate transformation paths, and classify samples that belong on the same transformation path.
翻译:深基因网络被广泛用于学习从低维潜层空间到高维数据空间的绘图。 在许多情况下, 数据转换是由这一潜层空间的线性路径来定义的。 但是, 潜层空间的欧几里德结构可能与数据中的潜在结构不匹配。 在这项工作中, 我们将一个基因多重模型纳入自动编码器的潜层空间, 以便从数据中学习低维多维结构, 并调整潜层空间以适应这一结构。 特别是, 我们侧重于数据从起始点开始、 返回到接近同一点的封闭转换路径的应用程序。 我们通过对自然封闭变形路径的数据进行实验, 显示该模型能够学习复杂系统的潜在动态, 生成变形路径, 并对属于同一变异路径的样本进行分类 。