Dataset Information

Tracking random walks.

ABSTRACT: In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them. We first discuss the ideal case of a constant sampling interval and short-tailed distributions of rest and move durations, and provide an exact analytical calculation of the fraction of correctly sampled trajectories. Further insights are obtained with simulations using more realistic long-tailed rest duration distributions showing that this fraction is dramatically reduced for real cases. We test our results for real human mobility with high-resolution GPS trajectories, where a constant sampling interval allows one to recover at best 18% of the movements, while over-evaluating the average trip length by a factor of 2. Using a sampling interval extracted from real communication data, we recover only 11% of the moves, a value that cannot be increased above 16% even with ideal algorithms. These figures call for a more cautious use of data in quantitative studies of individuals' movements.

SUBMITTER: Gallotti R

PROVIDER: S-EPMC5832728 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Publications

Tracking random walks.

Gallotti Riccardo R Louf Rémi R Luck Jean-Marc JM Barthelemy Marc M

Journal of the Royal Society, Interface 20180201 139

In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them. We first discuss the ideal case of a constant sampling interval and short-tailed distributions of rest and move durations, and p ...[more]

PMID: 29436509

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Project description:Large-scale network mining and analysis is key to revealing the underlying dynamics of networks, not easily observable before. Lately, there is a fast-growing interest in learning low-dimensional continuous representations of networks that can be utilized to perform highly accurate and scalable graph mining tasks. A family of these methods is based on performing random walks on a network to learn its structural features and providing the sequence of random walks as input to a deep learning architecture to learn a network embedding. While these methods perform well, they can only operate on static networks. However, in real-world, networks are evolving, as nodes and edges are continuously added or deleted. As a result, any previously obtained network representation will now be outdated having an adverse effect on the accuracy of the network mining task at stake. The naive approach to address this problem is to re-apply the embedding method of choice every time there is an update to the network. But this approach has serious drawbacks. First, it is inefficient, because the embedding method itself is computationally expensive. Then, the network mining task outcome obtained by the subsequent network representations are not directly comparable to each other, due to the randomness involved in the new set of random walks involved each time. In this paper, we propose EvoNRL, a random-walk based method for learning representations of evolving networks. The key idea of our approach is to first obtain a set of random walks on the current state of network. Then, while changes occur in the evolving network's topology, to dynamically update the random walks in reserve, so they do not introduce any bias. That way we are in position of utilizing the updated set of random walks to continuously learn accurate mappings from the evolving network to a low-dimension network representation. Moreover, we present an analytical method for determining the right time to obtain a new representation of the evolving network that balances accuracy and time performance. A thorough experimental evaluation is performed that demonstrates the effectiveness of our method against sensible baselines and varying conditions.

Dataset Information

Tracking random walks.

Publications

Tracking random walks.

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