Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of meth-ods called transformed subspace clustering (TSC). In order to account for non-linearity, ker-nelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.

中文翻译：

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变换子空间聚类

子空间聚类假设数据可分离到单独的子空间中。如此简单的假设并不总是成立。我们假设，即使原始数据不能分成子空间，也可以学习一种表示（转换系数），使得学习到的表示可以分成子空间。为了实现预期目标，我们将子空间聚类技术（局部线性流形聚类、稀疏子空间聚类和低秩表示）嵌入到变换学习中。整个配方是共同学习的；产生了一类新的方法，称为变换子空间聚类（TSC）。为了解决非线性问题，还提出了 TSC 的内核化扩展。为了测试所提出技术的性能，对图像聚类和文档聚类数据集进行了基准测试。