Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns phase invariant features which closely resemble receptive fields of complex cells in the visual cortex. Features trained on natural sounds however, rarely reveal phase invariance and capture other aspects of the data. This observation is a starting point of the present work. As its first contribution, it provides an analysis of natural sound statistics by means of learning sparse, complex representations of short speech intervals. Secondly, it proposes priors over the basis function set, which bias them towards phase-invariant solutions. In this way, a dictionary of complex basis functions can be learned from the data statistics, while preserving the phase invariance property. Finally, representations trained on speech sounds with and without priors are compared. Prior-based basis functions reveal performance comparable to unconstrained sparse coding, while explicitely representing phase as a temporal shift. Such representations can find applications in many perceptual and machine learning tasks.

利用稀疏编码学习语音数据的复杂表示，提出基于先验的基函数集合可以偏置相位不变的解决方案。与无约束稀疏编码的表现相当，同时明确地表示相位作为空间移位。这种表示方法可以在很多感知和机器学习任务中得到应用。

使用相位和幅度连续先验学习自然声音的稀疏复值表示