Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ RN that are of high dimension N but are constrained to reside in a low-dimensional subregion of RN. The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds, based on compressive sensing (CS) projection measurements. The statistical CS inversion is performed analytically. We derive the required number of CS random measurements needed for successful reconstruction, based on easily-computed quantities, drawing on block-sparsity properties. The proposed methodology is validated on several synthetic and real datasets.

中文翻译：

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使用因子分析器的非参数混合对流形进行压缩感知：算法和性能界限

非参数贝叶斯方法被用来构成低秩高斯的混合，对于高维 N 但被限制在 RN 的低维子区域中的数据 x ∈ RN。混合成分的数量及其等级是从数据中自动推断出来的。基于压缩传感 (CS) 投影测量，所得算法可用于学习流形和从流形重建信号。统计 CS 反演以分析方式执行。我们基于易于计算的数量，利用块稀疏特性，推导出成功重建所需的 CS 随机测量数量。所提出的方法在几个合成和真实数据集上得到了验证。