# A Noval Weighted Meta Graph Method for Classification in Heterogeneous Information Networks
## 1 Introduction  
In the real world, there exist lots of various entities, and together with their inter-relationships, they can be represented as information networks [1], such as Bibliographic Information Networks [2], Wikipedia [3], and Facebook. Existing studies [4; 5; 6; 7; 8; 9] mainly focus on representing and analyzing such systems using homogeneous information networks, which composed of one type of nodes and edges. For example, Figure 0(a) illustrates a co-author homogeneous network consisting of \"authors\" as nodes and \"publishing\" relationships as links. However, the real-world systems are usually complex, mixed-type, and heterogeneous which can be more realistically represented by heterogeneous information networks. For example, there are different kinds of objects such as accounts, blogs, and friends, and different types of links such as publishing, forwarding and commenting between different pairs of objects in social networks. As an example, Figure 0(b) shows a bibliographic information network composed of multi-typed objects. There are authors (A), conferences (C), and papers (P) as nodes, and different relationships such as \"publishing\" and \"writing\" between different pairs of nodes. One of the widely studied problems in Heterogeneous Information Networks (HINs) is classification considered as a semi-supervised learning approach, in which the labels of objects are predicted based on the structural properties or relationships between nodes. The classification can beapplied in different setting of applications of of HINs such as similarity search [1] and recommendation systems [10; 11]. One of the most popular concepts used to study HINs is meta path. The meta path can better preserve the relationship information between different types of entities in HINs in comparison to other broadly used concepts such as random walks. However, due to the inherent limitation of meta paths such as their length [1], they can only carry limited semantics. Another problem is that typical meta path generation approaches can produce many short paths or even isolated nodes which make processing and learning even less efficient [12]. To tackle the weaknesses of meta paths, in reference [13], the concept of meta graphs is proposed, which contain different meta paths together and are shown to be significantly more useful in various tasks. Different meta graphs contribute differently to specific classification problems. However, to the best of our knowledge, none of the existing methods has demonstrated different semantics among meta graphs. Here, we compute the weights of different meta graphs by a priori knowledge. On one hand, using labeled or annotated data can remarkably improve the classification performance, and on the other hand, acquiring labeled data or manual annotation of the available data is difficult and expensive. In this paper, we extend the labeled objects based on extending meta graphs and iteratively enlarge the training dataset. Finally, we use MCHIN to calculate the relatedness of multi-typed objects and group the objects into pre-specified classes by using the ranking distribution of objects. The contributions of this study are summarized as follows:  
* We identify more objects for the training sets by the Extension Meta Graphs in HINs, which can effectively utilize a priori knowledge and improve the performance of classification. * We introduce MCHIN which incorporates extension meta graphs' semantics and relevance measurement on objects and assigns categorical labels to each object by a ranking distribution function. * We apply our proposed model on three real-world datasets and conduct a comprehensive analysis of the proposed model to gain more insights. The results show the effectiveness of MCHIN in the classification task in comparison to other state-of-the-art methods. This paper is an extension of our previous conference paper \"CHIN: Classification with META-PATH in Heterogeneous Information Networks [9]\".