Streaming probabilistic tensor train decomposition

Effective numerical techniques, such as CANDECOMP/PARAFAC (CP) decomposition [10, 11, 12] and Tucker decomposition [13, 14] are the most commonly used tensor decomposition approaches and have been proposed to compress full tensors and to obtain their low-rank representations. CP decomposition approximates a tensor by a sum of rank-one tensors, while Tucker decomposition decomposes a tensor into a core tensor and several factor matrices. Since CP decomposition can be seen as a special case of Tucker decomposition [15], Tucker decomposition is more flexible than CP decomposition. However, due to the existence of a core tensor, Tucker decomposition also brings challenges in both modeling and computation. In this paper, we mainly focus on Tensor Train (TT) decomposition [16], which combines the advantages of CP and Tucker decomposition, because it provides a space-saving model called TT format while preserving the representation power. This paper is interested in the decomposition of streaming data. Due to the stress on database capacity and privacy, streaming data is generated continuously by different of data sources and in small sizes, such as log files from web application [17] and information from social networks [18]. Recently, several works decompose fast streaming data, e.g.