We present a new algorithmic framework, Intensity Profile Projection, for
learning continuous-time representations of the nodes of a dynamic network,
characterised by a node set and a collection of instantaneous interaction
events which occur in continuous time. Our framework consists of three stages:
estimating the intensity functions underlying the interactions between pairs of
nodes, e.g. via kernel smoothing; learning a projection which minimises a
notion of intensity reconstruction error; and inductively constructing evolving
node representations via the learned projection. We show that our
representations preserve the underlying structure of the network, and are
temporally coherent, meaning that node representations can be meaningfully
compared at different points in time. We develop estimation theory which
elucidates the role of smoothing as a bias-variance trade-off, and shows how we
can reduce smoothing as the signal-to-noise ratio increases on account of the
algorithm `borrowing strength' across the network.

本文提出了一种新的算法框架 —— 强度剖面投影，用于学习动态网络节点的连续时间表示，其特点是节点集和在连续时间内发生的瞬态交互事件的集合。我们的框架包括三个阶段：通过核平滑等方法估计节点对之间相互作用的强度函数；学习最小化强度重新构建误差的投影；并通过学习的投影归纳地构建演变中的节点表示。我们展示了我们的表示保留了网络的潜在结构，并且具有时间上的一致性，这意味着节点表示可以在不同的时间点进行有意义的比较。我们开发了估计理论，阐明了平滑作为偏差方差折衷的作用，并说明了如何随着信噪比的增加通过算法在网络中 “借力” 的方法来降低平滑度。

强度曲线投影：连续时间动态网络表示学习框架

Intensity Profile Projection: A Framework for Continuous-Time  Representation Learning for Dynamic Networks

In this paper an iterated function system on the space of distribution
functions is built. The inverse problem is introduced and studied by convex
optimization problems. Some applications of this method to approximation of
distribution functions and to estimation theory are given.

本文提出并研究了一个建立在分布函数空间上的迭代函数系统，并通过凸优化问题引入和研究了其逆问题。同时，本文还给出了该方法在分布函数逼近和估计理论方面的一些应用。