Abstract Dictionary learning for sparse representations has been successful in many reconstruction tasks. Simplicial learning is an adaptation of dictionary learning, where subspaces become clipped and acquire arbitrary offsets, taking the form of simplices. Such adaptation is achieved through additional constraints on sparse codes. Furthermore, an evolutionary approach can be chosen to determine the number and the dimensionality of simplices composing the simplicial, in which most generative and compact simplicials are favored. This paper proposes an evolutionary simplicial learning method as a generative and compact sparse framework for classification. The proposed approach is first applied on a one-class classification task and it appears as the most reliable method within the considered benchmark. Most surprising results are observed when evolutionary simplicial learning is considered within a multi-class classification task. Since sparse representations are generative in nature, they bear a fundamental problem of not being capable of distinguishing two classes lying on the same subspace. This claim is validated through synthetic experiments and superiority of simplicial learning even as a generative-only approach is demonstrated. Simplicial learning loses its superiority over discriminative methods in high-dimensional cases but can further be modified with discriminative elements to achieve state-of-the-art performance in classification tasks.

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进化单纯学习作为用于分类的生成式和紧凑型稀疏框架

摘要 稀疏表示的字典学习在许多重建任务中取得了成功。单纯学习是字典学习的一种改编，其中子空间被剪裁并获得任意偏移，采用单纯的形式。这种适应是通过对稀疏代码的附加约束来实现的。此外，可以选择一种进化方法来确定构成单纯形的单纯形的数量和维数，其中最有利于生成和紧致单纯形。本文提出了一种进化的简单学习方法作为用于分类的生成和紧凑稀疏框架。所提出的方法首先应用于一类分类任务，它似乎是所考虑的基准中最可靠的方法。当在多类分类任务中考虑进化简单学习时，会观察到最令人惊讶的结果。由于稀疏表示本质上是生成性的，因此它们存在一个基本问题，即无法区分位于同一子空间上的两个类。即使证明了仅生成方法，这一主张也通过合成实验和简单学习的优越性得到了验证。简单学习在高维情况下失去了对判别方法的优越性，但可以用判别元素进一步修改，以在分类任务中实现最先进的性能。它们存在一个基本问题，即无法区分位于同一子空间中的两个类。即使证明了仅生成方法，这一主张也通过合成实验和简单学习的优越性得到了验证。简单学习在高维情况下失去了对判别方法的优越性，但可以用判别元素进一步修改，以在分类任务中实现最先进的性能。它们存在一个基本问题，即无法区分位于同一子空间中的两个类。即使证明了仅生成方法，这一主张也通过合成实验和简单学习的优越性得到了验证。简单学习在高维情况下失去了对判别方法的优越性，但可以用判别元素进一步修改，以在分类任务中实现最先进的性能。