SageRank

Figure 1. A snapshot of the heterogeneous network in Eden. The thickness of the arrows indicate how early the action happens. The earlier the actions, the thicker are the arrows, and the stronger are the connections between Circles and Users. The thickness of the Index arrow is proportional to the net influence of the Circle.

In addition to SageMint, Eden is powered by SageRank, a dynamic interests ranking system. Inspired by Google’s PageRank, SageRank models the structure and evolution of the user-Circle interaction graph. Our heterogeneous dynamic graph embedding projects the social network, user activity, and Circle content to a high-dimensional space where similar users and Circles are close to each other in this vector space. Eventually, SageRank increases user engagement, Circle engagement, and boosts our effort to index the web.

SageRank evaluates the quality and potential impact of Circles, Users, Webpages, and Interests. All of these entities and their relationships can be Modeled as a dynamic heterogeneous network graph $G=(V;Z;E)$. $V=\{v_1, ..., v_n\}$ is a set of unique vertices (i.e. nodes) in the graph. An object type mapping function $f_v: V\rightarrow O$ maps each $v_i\in V$to one of the 4 categories of objects:

$O=\{O_O, O_U,OM, O_G\}$ which are respectively Circle, User, Webpages, and Interests. $Z=\{z_1, ..., z_n\}$ corresponds to the property of each vertex $\{v_1, ..., v_n\}$. $Z_O=\{z_i:f(v_i)=O_O\}$ is the set of Circle properties, which include opinion content, activity, and Circle-related rewards.

$Z_U=\{z_i:f(v_i)=O_U\}$is the set of User properties, which include user profile, total number of predictions, prediction accuracy rate, and the number of tokens they own.

$Z_M=\{z_i:f(v_i)=O_M\}$ is the set of Webpage properties, which include webpage description, traffic volume, past interactions, and other related values. $Z_G=\{z_i:f(v_i)=O_G\}$ is the set of Interest properties, which include daily average number of posts, total participants, and daily average number of new members.

Furthermore, $E=\{e_1, ..., e_m\}$ is a set of all unique edges in the network. Each edge $e_k$ is a quadruple $e_k=(v_i, v_j, t_{ij}, w_{ij})$. Where $v_i,$ and $v_j$ are the source/destination nodes, and $t_{ij}$ is the timestamp of the creation of this edge. $w_{ij}$ is the property of this edge. For instance, $e_k$ can represent a user $v_i$ joins an Circle $v_j$ at time $t_{ij}$, with the detailed interaction encoded in $w_{ij}$. A relationship mapping function $f_e: E\rightarrow R$ maps each edge to one of the six relationship types $R=\{R_M, R_P, R_B, R_A, R_J, R_L\}$ which are respectively Index, Purchase, Mint, Merge, Join, and Link. A simplified binary edge set $E^-=\{e^-_1, ..., e^-_m\}$ contains binary indication of the connection from $v_i$ to $v_j$ at time $t_{ij}$ without the property $w_{ij}$. The core of SageRank is a link prediction function $f_p:G_{t\leq \tau} \rightarrow E^-_{\tau+1}\backslash \{e_i: f_e(e_i)=R_M\}$ , i.e. given the graph $G_{t\leq \tau}$ prior to time $\tau$, predict all the binary edges except Index at timestep $\tau + 1$. The objective only predicts the binary edges to simplify the prediction task. Index is excluded because it is an exogenous action initiated by users which our recommender system cannot influence.

SageRank starts its computation with selecting seed users who have an outstanding track record in indexing the web, and their indexing and purchasing behaviors of Circles will be taken as a signal to help us identify high quality Circles. At this stage, only the subgraph that contains the direct (one-hop) neighbors of the seed users and the seed users themselves will be embedded.

The authorship, indexing, or early investment of the high quality Circles helps us further identify even more credible and knowledgeable users. By random walks on the social network of users and Circles, SageRank iteratively updates its estimation of the credibility of quality of the users and Circles. Such estimation will be combined with language embedding on the Circles, social network embedding, and user behaviors (e.g. click streams, searches, and interests) to form as an input into a Hybrid Deep Recommender System (HDRS) that will optimizes the recommended Circles and Interests to users whose interest are most likely to be aligned with. HDRS helps Circles to get more traction and users discover the most valuable and interesting content, and the improved user experience can further boost the social and trading activity on our platform.