Generic method Using participant-votes data, it is possible to predict future votes as follows: Use a tensor to store participant-votes data, one slice per positive/negative/pass votes. Use modified tensor decomposition such as CP to derive latent matrices, as follows: When updating the elements of the latent matrices, evaluate their fitness using a weight matrix. The weight elements should be 1 when the observation is present in the same place in participant-votes data 0 when the observation is missing (i.e. link to be predicted)

title Pol.is Analysis / Stochastic block models description Stochastic block models https://arxiv.org/abs/1501.06444 Stochastic block models for multiplex networks  can give you the probability that a given node belongs to a given cluster/block over all 3 layers (agree/pass/disagree), without squishing the different relationships into one. > home

title Pol.is Analysis / Multiplex layer distance description Multiplex layer distance https://iopscience.iop.org/article/10.1088/1367-2630/ab14b3 Here the authors suggest that if you use any type of centrality measure in each network layer (e.g. degree centrality for the positive-answers layer and 'inverse degree' centrality for the negative-answers) but convert it into 'rank'... ... you can work in a unifying way over all layers and eg define a sort of distance  between them.

Citation graph Legend digraph cg { article; book [shape = rectangle]; important [penwidth = 3]; } digraph cg { horvat2012 [penwidth = 3];

title Pol.is Analysis / Graph generation model description Graph generation model We assume discrete time and that no two users arrive simultaneously at the poll, i.e. one user arrives at time $t$ and the other at time ${t^{'}}$, such that $t < {t^{'}}$. At time $t = 0$, we have $\left| {{U_0}} \right| = 0,\left| {{V_0}} \right| = n_0^v,\left| {{E_0}} \right| = 0$. This reflects the fact that the poll starts with no users, a set of initial statements and no votes. At time $t-1$, we consider the graph ${G_{t-1}} = ({U_{t-1}},{V_{t-1}},{E_{t-1}})$ as described in the previous section. At each time $t$, either a new user ${u_t} \notin {U_{t - 1}}$ participates in the poll (such that ${u_t} \cup {U_{t - 1}} = {U_t}$) or an existing user $u \in {U_{t - 1}}$ returns.

title Pol.is Analysis / Definitions description Definitions Let ${G_t} = ({U_t},{V_t},{E_t})$ be a bipartite graph[2] representing a poll at time $t$. For every user $u$ that has participated in the poll by time $t$, there is a node $u \in U_t$. Respectively, for every statement $v$ that is part of the poll by time $t$, there is a node $v \in V_t$. If a user $u$ has voted on some statement $v$, then an edge $(u,v) \in {E_t}$ exists. We distinguish between three types of edges: those belonging to positive ("agree"), negative("disagree") and neutral ("pass") votes, represented with $E_t^ + ,E_t^ - ,E_t^0$ respectively ($E_t^ +  \cup E_t^ -  \cup E_t^0 = {E_t}$). When a user votes for a statement, an appropriate edge is being created, depending on the type of the vote (positive, negative or neutral).  We treat this graph as a multiplex network[3] with three layers , where the layers are being defined by the three types of edges (edges of a type reside all in the same layer), all nodes are common among all layers, and there are no interlayers edges. We will be using the formal notation of multiplex networks only when strictly necessary. To simplify further, the edge sets $E_t^ + ,E_t^ - ,E_t^0$ will be used to represent the layers they belong to, where it is clear from context that we refer to the one or the other. 

title Pol.is Graph Theoretic Modeling description Formalizing the Pol.is graph :::info If you're reading this, you're welcome to contribute! 🎉 For existing pages: Make use of comments and ample +1s. Edit text directly if you find inaccuracies.

Promise Delivery

Promise Graph theoretic work Delivery Check upstream bibliography

Promise Bayesian non-parametric method to infer both latent features and which entities have which feature. Application : link prediction Delivery One author is a psychologist = accessible text to non experts. Good intro into latent feature approaches.

A tensor decomposition technique that can be used for link prediction in a dynamic graph. Focus on 3 dimensions (third-order tensor), where the first two can be the adjacency matrix and the third the time. Practical results come from the CP (CanDecomp /ParaFac) technique, which is an approximation of the tensor decomposition. Simple, effective. Delivery Simply written, delivers as promised. Good introduction to tensor decomposition.

# zhu2016

Promise A simple and flexible mechanism for link prediction: time series out of any node similarity metric + forecasting. Delivery Delivers the goods + bonus points on simplicity.

Promise A survey of link prediction algorithms. Emphasis on machine learning (presumably because it's the latest application at the time of writing). Delivery