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Periodicity is one of the most frequently occurring phenomena for moving objects. Animals usually have periodic movement behaviors, such as daily foraging behaviors or yearly migration behaviors. Such periodic behaviors are the keys to understand animal movement and they also reflect the seasonal, climate, or environmental changes of the ecosystem. However,… (More)

- Zhenhui Li, Jiawei Han
- 2013

As spatiotemporal data becomes widely available, mining and understanding such data have gained a lot of attention recently. Among all important patterns, periodicity is arguably the most frequently happening one for moving objects. Finding periodic behaviors is essential to understanding the activities of objects, and to predict future movements and detect… (More)

1 Proof of Theorem 1 Theorem 1. Let Y ∈ R n×m be a matrix where each column is an eigenvector of eigen-problem Ly = λDy. If there exists a matrix A ∈ R d×m and p where p ∈ {0, 1} d , p T 1 = m such that X T diag(p)A = Y, then each column of A is an eigenvector of eigen-problem diag(p)XLX T diag(p)a = λdiag(p)XDX T diag(p)a with the same eigenvalue λ. Proof.… (More)

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