Publication

Convolutional Neural Networks on Graphs and Stationarity

2016
Student Projects

Abstract

The Fourier spectrum is often not sufficient to discriminate complex signals because it does not take into account higher-order moments. Wide Sense Stationarity is for sure not sufficient to characterize the signal as it considers only moments of order 2. The question we try to answer in this project is: does a graph convolutional neural network stationaries data, i.e., transform then non-linearly such that they become stationary?

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2016
Student Projects

Abstract

Official source

Related concepts (25)

Stationary process

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. If you draw a line through the middle of a stationary process then it should be flat; it may have 'seasonal' cycles around the trend line, but overall it does not trend up nor down.

Convolutional neural network

Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels.

Time series

In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart).

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Convolutional Neural Networks on Graphs and Stationarity

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