Welcome!
Thank you for being here.
- Part 1- PCA: Dimensionality reduction of the dataset with principal component analysis.
- Part 2-State space reconstruction: Build a maximally predictive posture sequence matrix using delay-embedding.
- Part 3- Transition Matrix Clustering: Build the transition matrix and analyze one of its eigenvectors.
The three parts are best done in order for a smooth experience, but they technically can be run independently. You could substitute any dataset you have in the tutorial, pending some small modifications to the code.
The theoretical framework and code from Parts 2 and 3 are from Antonio C. Costa (École Normale Supérieure de Paris). All the functions for embedding and transition matrices are his as well. This work has been done under the supervision of Greg J. Stephens (Okinawa Institute of Science and Technology and Vrije Universiteit Amsterdam).
Colab notebooks:
- Part 1- PCA.ipynb
- Part 2-State space reconstruction.ipynb
- Part 3- Transition Matrix Clustering.ipynb
Extra functions:
- clustering_methods.py
- delay_embedding_1D.py
- operator_calculations.py
- stats.py
Pictures and videos from the text:
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img_angles_calculation.png
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img_larva_svd0_vs_ant_angle_vs_phi1.png
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img_measurement_matrix.png
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img_trajectory_matrix.png
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img_transition_matrix_schematics.png
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img_umap_celegans_costa.png
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vid_intro_state_space_Sugihara.mp4
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vid_larva_experiment_Irina_Korshok.mp4
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vid_phase_space_pendulum_Ghrist_Math.mp4
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vid_Takens_thm_Sugihara.mp4
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vid_tracked_larva_segments.mp4
Data files:
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file_angles_larva.csv
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file_principal_components_time_series_larva.csv