Table 1 Notations used in this paper

\({\mathcal{D}} = \left\{ {d_{i} |i\, = \,\overline{1,Q} } \right\}\)

The set of reviews’ text, where Q is the number of reviews

\({\mathcal{Y}} = \left\{ {y_{i} |i\, = \,\overline{1,Q} } \right\}\)

The set of overall rating, y_i is overall rating corresponded with d_i

\({\mathcal{A}} = \left\{ {a_{1} ,a_{2} , \ldots ,a_{K} } \right\}\)

The set of aspect, where K is the number of aspects

\({\mathcal{C}}_{\text{j}} \, = \,\left\{ {w_{j1} ,w_{j2} , \ldots ,w_{jN} } \right\}\)

The set of associated core terms for aspect a_j, where N is the number of words

\({\mathcal{V}}\, = \,\left\{ {{\text{w}}_{\text{k}} |{\text{ k}}\, = \,\overline{{1,{\text{P}}}} } \right\}\)

The corpus of words, where P is the number of words

\({\mathcal{S}}_{\text{j}} \, = \,\left\{ {{\text{s}}_{\text{j1}} ,{\text{s}}_{\text{j2}} , \ldots ,{\text{s}}_{\text{jM}} } \right\}\)

The set of sentences are assigned aspect a_j, where M is the number of sentences

\({\mathcal{T}}_{\text{j}} \, = \,\left\{ {w_{j1} ,w_{j2} , \ldots ,w_{jT} } \right\}\)

The set of aspect words are aspect expressions, where \({\mathcal{T}}_{\text{j}}\) is the expression for aspect a_j, and T is the number of words

\({\mathbf{i}}_{\text{j}} \in {\mathbb{R}}^{\text{K}}\)

The aspect rating inferred from review d_i over K aspect, r_i = (\(r_{{i_{1} }} ,r_{{i_{2} }} , \ldots r_{{i_{K} }}\))

\({\varvec{\upalpha}}_{\text{i}} \in {\mathbb{R}}^{\text{K}}\)

The aspect weights user places on K aspect within reviews’ text d_i, \({\varvec{\upalpha}}_{\text{i}} = \left( {\alpha_{{i_{1} }} ,\alpha_{{i_{2} }} , \ldots ,\alpha_{{i_{K} }} } \right)\)

\({\text{y}}_{\text{i}} \in {\mathbb{R}}^{ + }\)

The overall rating of review d_i

\(r_{{i_{j} }}\)

The aspect rating on j-th aspect of review i, \(r_{{i_{j} }}\) ∈ [1,5]

\(\alpha_{{i_{j} }}\)

The aspect weight of j-th aspect of review i, \(\alpha_{{i_{j} }}\) ∈ [0,1]