This paper aims to provide an unsupervised modelling approach that allows for
a more flexible representation of text embeddings. It jointly encodes the words
and the paragraphs as individual matrices of arbitrary column dimension with
unit Frobenius norm. The representation is also linguistically motivated with
the introduction of a novel similarity metric. The proposed modelling and the
novel similarity metric exploits the matrix structure of embeddings. We then go
on to show that the same matrices can be reshaped into vectors of unit norm and
transform our problem into an optimization problem over the spherical manifold.
We exploit manifold optimization to efficiently train the matrix embeddings. We
also quantitatively verify the quality of our text embeddings by showing that
they demonstrate improved results in document classification, document
clustering, and semantic textual similarity benchmark tests.

本文提出了一种无监督建模方法，通过引入新的相似度度量和矩阵嵌入的优化问题，可以更加灵活地表示文本嵌入，并在文档分类、文档聚类和语义文本相似性基准测试等方面得到改进的结果。