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.

翻译：本文旨在提供一种不受监督的建模方法,以便能够更灵活地代表嵌入的文字;将文字和段落作为任意柱体的单个矩阵,与单位Frobenius规范编码成一个任意柱体维度的单项矩阵;还以语言为动力,采用新的相似度衡量标准;拟议的建模和新颖相似度衡量标准利用嵌入的矩阵结构;然后我们继续表明,同样的矩阵可以重新形成单位规范的矢量,并将我们的问题转化为球体的优化问题;我们利用多重优化来有效地培训矩阵嵌入;我们还通过显示在文件分类、文件组合和语义相似性基准测试方面的结果有所改善,对文本嵌入的质量进行定量核查。