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Similarity enhancement of heterogeneous networks by weighted incorporation of information

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Abstract

In many real-world datasets, different aspects of information are combined, so the data is usually represented as heterogeneous graphs whose nodes and edges have different types. Learning representations in heterogeneous networks is one of the most important topics that can be utilized to extract important details from the networks with the embedding methods. In this paper, we introduce a new framework for embedding heterogeneous graphs. Our model relies on weighted heterogeneous networks with star structures that take structural and attributive similarity into account as well as semantic knowledge. The target nodes form the center of the star and the different attributes of the target nodes form the points of the star. The edge weights are calculated based on three aspects, including the natural language processing in texts, the relationship between different attributes of the dataset and the co-occurrence of each attribute pair in target nodes. We strengthen the similarities between the target nodes by examining the latent connections between the attribute nodes. We find these indirect connections by considering the approximate shortest path between the attributes. By applying the side effect of the star components to the central component, the heterogeneous network is reduced to a homogeneous graph with enhanced similarities. Thus, we can embed this homogeneous graph to capture the similar target nodes. We evaluate our framework for the clustering task and show that our method is more accurate than previous unsupervised algorithms for real-world datasets.

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Notes

  1. https://www.imdb.com/.

  2. https://dblp.uni-trier.de/.

  3. developer.twitter.com.

Abbreviations

\(\mathcal {N}\) :

Target set

\(\mathcal {A}_i\) :

Information set

\(\mathcal {M}\) :

Main attribute set

\(\mathcal {R}\) :

Relational attribute set

\(\mathcal {T}\) :

Textual attribute set

C :

Clustered set

\(t_j\) :

Text object

\(\textbf{t}_j\) :

Word vector of \(t_j\)

\(\mathbf {t_j^e}\) :

Embedded vector of \(t_j\)

\(\overrightarrow{\textsf {BERT}}(.)\) :

BERT embedding function

\(\textsf {TF}(.)\) :

Rank weighted density function

\(m_j\) :

Number of elements of \(t_j\)

\(\textrm{t}_i^j\) :

i-th word of vector \(\textbf{t}_j\)

\(\textrm{x}_{ih}^j\) :

h-th element of \(\overrightarrow{\textsf {BERT}}(\textrm{t}_i^j)\)

\(\mathcal {B}_h^j\) :

h-th element of \(\mathbf {t_j^e}\)

\(\mathbb {D}\) :

Feature space size

\(\mathbb {f}(.)\) :

Term frequency in target set

\(\mathbb {H}(.)\) :

Term frequency in feature space

\(\mathbb {L}(.)\) :

Text length

\(G =(\mathcal {V}, \mathcal {E}, \mathcal {W})\) :

Star heterogeneous graph

\(G_c=(\mathcal {V}_c, \mathcal {E}_c, \mathcal {W})\) :

Core graph

\(G_s^i=(\mathcal {V}^{i}_s, \mathcal {E}^{i}_s,\mathcal {W})\) :

\(\mathcal {M}_i\) shell graph

\(\overline{G}_{c}=(\mathcal {V}_c, \mathcal {E}_c, \overline{\mathcal {W}})\) :

Homogeneous core graph

\(V_\mathcal {N}\) :

Vertex of target set

\(V_\mathcal {M}\) :

Vertex of main attribute set

\(E_\mathcal {I}\) :

Internal link set

\(E_\mathcal {O}\) :

External link set

\(d_{xy}\) :

Euclidean distance of x, y

\(w_\mathcal {R}(.,.)\) :

Relational weight

\(w_\mathcal {T}(.,.)\) :

Textual weight

\(w_\mathcal {J}(.,.)\) :

Joint presence weight

w(., .):

Total weight

\(p({{\mathcal {M}}_i})\) :

\({{\mathcal {M}}_i}-\)path

\(\rho \langle .,p({{\mathcal {M}}_i}),.\rangle \) :

\({\mathcal {M}}_i\) auxiliary path

\(\rho _i\langle .,.\rangle \) :

\({\mathcal {M}}_i\) shortest path

\(\mathcal {R}(G)\) :

Remapped graph

\(\pi (.)\) :

Remapped function

\(W(.), \overline{W}(.)\) :

Path weight function

\(\mathcal {H}\) :

Spanner graph

\(P_i=\{c_i, \sigma _i, \kappa _i\}\) :

Truncation parameters

\(\alpha =\{\alpha _\mathcal {R}, \alpha _\mathcal {T}, \alpha _\mathcal {J}\}\) :

Weighting coefficients

\(\beta _i\) :

Main attribute impact factor

\(\theta _i\) :

Scaling parameter

\(\mu _i\) :

Spanner parameter

\(\mathbb {N}\) :

Normalization operator

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Author notes

  1. Fatemeh Baharifard and Vahid Motaghed have equally contributed to this work.

Authors and Affiliations

  1. School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    Fatemeh Baharifard & Vahid Motaghed

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  1. Fatemeh Baharifard
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Baharifard, F., Motaghed, V. Similarity enhancement of heterogeneous networks by weighted incorporation of information. Knowl Inf Syst 66, 3133–3156 (2024). https://doi.org/10.1007/s10115-023-02050-x

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