Spectral Methods

Vidal, René; Ma, Yi; Sastry, S. Shankar

doi:10.1007/978-0-387-87811-9_7

Cited by 1 publication

(1 citation statement)

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“…Eigen decomposition retrieves the structures of the data cloud in the high-dimensions space by decomposing it into a set of eigenvalues and eigenvectors. Eigenvectors are orthogonal unitarian column vectors, ordered according to their eigenvalues (Vidal, Ma and Sastry, 2016), which represent dimensions of the data cloud: the first eigenvector identifies the dimension of the largest variance in the data, the second one the second largest variance, and so on. By identifying the most relevant eigenvectors of a movement data set represented as sequences of states of an individual, eigen decomposition can find commonly repeated behavioural patterns, the so-called eigenbehaviours (Eagle and Pentland, 2009).…”

Section: Introductionmentioning

confidence: 99%

Using eigen decomposition and sequence-based representation to extract movement patterns from contextualized tracking data

Brum-Bastos

Long

Demšar

2021

AGILE GIScience Ser.

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Abstract. State sequences are a new paradigm to encode and represent contextualised movement data. A state sequence is a temporal succession of characters representing categorical states of the moving entity or its surrounding environment. Eigen decomposition, a principal components analysis method, is an option to reduce and find patterns in such multi-dimensional categorical data through dimensionality reduction. Recurrent patterns can be found by identifying the most relevant eigenbehaviours, which are a set of vectors that characterize the variation in the behaviour of an entity during a time period. Dimensionality reduction techniques have so far not been widely used in movement analytics and in this paper we demonstrate how they could help analyse responses of a moving entity to the dynamic environmental conditions. Specifically, we use sequence-based representation and eigen decomposition to investigate movement patterns of maned wolves (Chrysocyon brachyurus) in relation to vegetation vigour in their habitat. We use a set of GPS-trajectories from a group of maned wolves to which we link multi-source NDVI data as a proxy for the state of vegetation. We find that eigenbehaviours can identify patterns in the wolves’ responses to dynamic environmental conditions that align with the current literature on the species. Our research highlights the potential for dimensionality reduction and sequence-based methods to identify patterns in large tracking databases linked to contextual data.

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Section: Introductionmentioning

confidence: 99%