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Density-based histogram of singular values for √ n ˆ L andˆNandˆ andˆN / √ n for the animal movement data in blue bars and the theoretical predictions associated with the improvement clustering with K = 10 as the red line and with K = 100 as the purple dashed line.

Density-based histogram of singular values for √ n ˆ L andˆNandˆ andˆN / √ n for the animal movement data in blue bars and the theoretical predictions associated with the improvement clustering with K = 10 as the red line and with K = 100 as the purple dashed line.

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Fig. 3. A screenshot from movebank displaying the raw GPS data.
Fig. 5. Density-based histogram of singular values for √ n ˆ L for the...
Fig. 7. Density-based histogram of singular values for √ n ˆ L...
Fig. 11. (left) The singular value density ofˆNofˆ ofˆN for a simulated...
Fig. 12. A plot of the matrix {1[ ˆ Fij > 0]}i,j , where the rows and...
Detection and Evaluation of Clusters within Sequential Data
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  • Oct 2022
Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these fa...
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Context 1
... short: the algorithm detects geographical features and movement patterns, and the algorithm does so based on the sequential data alone, i.e., it captures behavior of the animals. Figure 7 next compares the spectral noise of (10) and (25) to the theoretical predictions for BMCs (recall Proposition 2). ...
Context 2
... example, the distribution of singular values depicted in Figure 7 is not predicted perfectly. This is likely caused by the symmetry assumption between states within a BMC, which is at odds with the geographical structure of the data. ...