Graph-structured data appears in many modern applications like social networks, sensor networks, transportation networks and computer graphics. These applications are defined by an underlying graph (e.g. a social graph) with associated nodal attributes (e.g. number of ad-clicks by an individual). A simple model for such data is that of a graph signal--a function mapping every node to a scalar real value. Our aim is to develop signal processing tools for analysis of such signals de- fined over irregular graph-structured domains, analogous to classical Fourier and Wavelet analysis defined for regular structures like discrete-time sequences and two-dimensional grids.

In this work, we start by reviewing the notion of a Graph Fourier Transform (GFT), which has been defined in the literature for graph signals. We examine the spatial and spectral features of circulant graphs, which accommodate linear shift-invariant operations. We describe fundamental operations such as shifting, sampling, graph-reconnection and linear filtering for signals on circulant graphs and derive associated sampling and graph-reconnection theorems. We also develop wavelet filter bank structures for multi resolution analysis of large-scale graphs.

We present a method to decompose an arbitrary graph into a linear combination of circulant graphs. This helps extend fundamental operations such as sampling, filtering and multi resolution filter banks to general graphs. We present an application in the area of graph semi-supervised learning where some of the existing algorithms can be viewed as suitably designed filters defined in the GFT domain. We propose a wavelet regularized learning algorithm and evaluate the performance on some real-world datasets.

With the advent of ubiquitous mobile sensing and self-tracking groups, travel demand researchers have a unique opportunity to combine these two developments to improve the state of the art of travel diary collection. While the use of mobile phones and the inference of travel diaries from GPS and sensor data allows for lower-cost, longer surveys, we show how the self-tracking movement can be leveraged to interest people in participating over a longer period of time. By compiling personalized feedback and statistics on participants’ travel habits during the survey, we can provide the participants with direct value in exchange for their data collection effort. Moreover, the feedback can be used to provide statistics that influence people’s awareness of the footprint of their transportation choices and their attitudes, with the goal of moving them toward more sustainable transportation behavior.

We describe an experiment that we conducted with a small sample in which this approach was implemented. The participants allowed us to track their travel behavior over the course of two weeks, and they were given access to a website they were presented with their trip history, statistics and peer comparisons. By means of an attitudinal survey that we asked the participants to fill out before and after the tracking period, we determined that this led to a measurable change in people’s awareness of their transportation footprint and to a positive shift in their attitudes toward sustainable transportation.

With the advent of ubiquitous mobile sensing and self-tracking groups, travel demand researchers have a unique opportunity to combine these two developments to improve the state of the art of travel diary collection. While the use of mobile phones and the inference of travel diaries from GPS and sensor data allows for lower-cost, longer surveys, we show how the self-tracking movement can be leveraged to interest people in participating over a longer period of time. By compiling personalized feedback and statistics on participants’ travel habits during the survey, we can provide the participants with direct value in exchange for their data collection effort. Moreover, the feedback can be used to provide statistics that influence people’s awareness of the footprint of their transportation choices and their attitudes, with the goal of moving them toward more sustainable transportation behavior.

We describe an experiment that we conducted with a small sample in which this approach was implemented. The participants allowed us to track their travel behavior over the course of two weeks, and they were given access to a website they were presented with their trip history, statistics and peer comparisons. By means of an attitudinal survey that we asked the participants to fill out before and after the tracking period, we determined that this led to a measurable change in people’s awareness of their transportation footprint and to a positive shift in their attitudes toward sustainable transportation.