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SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application.

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Presentation on theme: "SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application."— Presentation transcript:

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2 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 1/00 Combined Distance and Feature-Based Clustering of Time-Series: An Application on Neurophysiolohy George Potamias Institute of Computer Science FORTH Heraklion, Crete SETN 2002 April 10-12 2002 Thessaloniki, Greece

3 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 2/00 Brain development: Series of events cell proliferation and migration, growth of axons and dendrites, formation of functional connections and synapses, cell death, myelination of axons and refinement of neuronal specificity Adult brain: Complex network of fibers Brain nuclei functional structures Knowledge of the underlying mechanisms that govern these complex processes, and the study of histogenesis and neural plasticity during brain development are critical for the understanding of the function of normal or injured brain. The Application Domain

4 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 3/00 The late embryonic development of avian brain was selected for this study; Biosynthetic activity, such as protein synthesis, underlies brain-development events. The history of in vivo protein synthesis activity of specific brain areas could: yield insight on their pattern of maturation reveal relationships between distantly located structures suggest different roles of the topographically organized brain structures in the maturation processes Avian Brain Study: The time course of protein-synthesis activity of individual brain areas as a model to correlate critical periods during development Goal: Extract critical-relationships that govern the normal ontogenic processes ? Study & Goal

5 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 4/00 The late embryonic development between day 11 (E11) and day 19 (E19) as well as the post-hatching day 1 (P1) was studied During that time proliferation of neurons has ceased and cell growth, differentiation, migration and death, axon elongation, refinement of connections, and establishment of functional neuronal networks occurs Biomedical Background For the determination of biosynthetic activity the in vivo auto-radiographic method of carboxyl labeled L-Leucine was used (an essential amino acid present in most proteins) The experimental data concern 30 chick embryos

6 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 5/00 Time-Series Representation 49 brain-areas (nuclei) were identified. Autoradiographic film Image Analysis Intensities For each area, the means over all chicks were recorded Intensities Protein Synthesis Patterns Days The final outcome is a set of 49 time-series in a time-span of 6 time-points (five embryonic days and one post-hatching day)

7 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 6/00 How to get meaning from the mesh ? How to get indicative developmental patterns ? The Problem

8 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 7/00 Time-Series discretization Compute distances (similarities) Method: Discovery of Coherences between Time Series models Induce underlying/hidden models|| Brain Development Hierarchy models Induce underlying/hidden models|| Brain Development Hierarchy Distance & feature-based Hierarchical Clustering Distance & feature-based Hierarchical Clustering Time Series collection hierarchical … need for hierarchical modeling Visualize – Interpret clustering result(s) Visualize – Interpret clustering result(s)

9 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 8/00 Need for an adjustable and adaptive time-series matching operation not-significant parts Ignore small or not-significant parts Translate the offset align vertically Amplitude scaling fixed width Time-Series Matching: Problems & Tasks … apply matching metric Use of a normal distance metric … outliers; different scaling factors and baselines ?

10 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 9/00 Achieves- in a convenient way, amplitude scaling, vertical-alignment and identification of (non) significant parts. Time-Series Discretization v2 v4 v1 v3 …… v1: drastic-increase v2: increase v3: decrease v4: drastic-decrease 4 4 intervals = 4 4 nominal values QDT: QDT: Qualitative Discrete Transformation discrete value A new continuous value will be assigned to the same discrete value as its preceding values if the continuous value belongs to the same population (based on statistical-significance testing). … the number of discrete-intervals to be specified by the user Lopez et.al., 2000

11 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 10/00 Discretization specifics For a time-series T: {X 1, X 2, …, X n } s : number of discrete values w idth = v i = discr (Xi) = Discrete Transform of T T: {v 1, v 2, …, v m }

12 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 11/00 Distance Metric dist(T a,T b ) = distance(v a;i, v b;i ) = DTW Segmentation …

13 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 12/00 Graph Theoretic Hierarchical Clustering: The Basics Iterative Partitioning form … which sub-group to form? stop … when to stop? Nodes Time-Series Nodes Edge TS distance weighted Edge dist(T a,T b ) weighted Graph Fully connected weighted Graph Minimum Spanning Tree preserves the minimum distance between time-series offers the ability to isolate and group nodes STOP Hierachical Clustering Category Utility Category Utility: A probabilistic metric

14 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 13/00 Category Utility Distribution of Feature-Values CLUSTERED … if CLUSTERED Distribution of Feature-Values NOT-clustered … if NOT-clustered Over ALL formed clusters # formed clusters

15 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 14/00 Stopping CriterionG11 G12 G21 G22 CU(G11,G12) > CU(G21,G22) G111G112 Current Best Current Best CU(G111,G112,G12) < Previous Best CU(G11,G12) STOP Current Best Current Best CU(G121,G122,G11) > Previous Best Previous Best CU(G11,G12) continue G11 G12 Best Best Partitioning G122 G121

16 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 15/00 GTC - Graph Theoretic Clustering: The Procedure ~O(n 2 F V) (preliminary)…… STOP HierarchicalClustering-Tree

17 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 16/00 AM, Ad, Bas, Cpi, DM, GCt, HV, Hip, Co, POM, SL, Tn, Lli, PP, Imc, SCA 16 c3 Ac, CDL, DL, FPLp, GLv, IO, MM, N, NI, OcM, Ov, Rt, SM, Slu, Tov, nBOR, Loc, PA, PM, RPO 20 c2 CA, CP, E, FPLa, LC, LPO, Mld,PL, PT, SP, Spi, TPc,VeM 13 c1 Brain Nuclei (areas)# ObjectsCluster no mean The biosynthetic activities of each clusters brain-areas- over the stamped developmental ages, exhibit no statistical- significant deviation from the respective mean of the cluster Patterning Brain Developmental Events: The Clusters mean So, the mean of each cluster offers an indicative and representative model for the brain-developmental events … induction of critical relationships induction of critical relationships between the brain areas

18 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 17/00 Decrease – Increase C1: Decrease – Increase Decrease C2: Decrease Increase C3 : Increase Patterning Brain Developmental Events: The Patterns

19 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 18/00 Patterning Brain Developmental Events: Hierarchical-Tree Critical Relationships c2 c3 c1 c2 c3 late maturationearly early early maturation control or, control

20 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 19/00 Patterning Brain Developmental Events: Biomedical Interpretation c1 c2 Clusters {c1} {c2} sensory limbic Second order sensory and limbic areas migration Decline in protein-synthesis cell death or cell displacement due to migration represent a common phenomenon in many brain regions under development Differ significantly at post-hatching day c1 {c1}: receive sensory-input increase c2 {c2}: leucine-incorporation is decreased c3 Cluster {c3} Somatosensorymotor white-matter Somatosensory, motor, and white-matter areas myelination Increase in protein-synthesis myelination and motor-activity motor-activity

21 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 20/00 Conclusion & Future work QDTGTC The introduced time-series mining methodology (QDT/GTC), and the respective analysis on the history of in vivo protein synthesis activity of specific brain areas, yields insight on their maturation patterns and reveal relationships between distantly located structures The presented study contribute to the identification of common origin of brain structures and provide possible homologies in the mammalian brain Inclusion of additional formulas and procedures for computing the distance between time-series Experimentation on other application domains in order to validate the approach and examine its scalability to huge collections of time-series (initial experiments on economic time- series are already in progress with encouraging preliminary results)

22 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 21/00 GTC on ASL Australian Sign Language dataset A subset of the dataset for words: spend, lose, forget, innocent, norway, happy, later, eat, cold, crazy Keogh and Pazzani, 1999 3 rd Conf. on Principles & Practice of Knowledge Discovery in Databases one vs. another............ word-1word-2 2Euclidean 22DTW 21SDTW 25QDT/GTC out of 45

23 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 22/00 The Distance Metric: Intra-Characteristics of TS G. Potamias, Institute of Computer Science, FORTH C. Dermon, Dept. of Biology, University of Crete NNESMED 2001 22/ 12 Time-to-time percentage changes Capture trend / evolution Alignment vertically (offset) Amplitude scaling Statistical-significance of a change Capture important parts of TS

24 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 23/00 Importance / weight of a change … with respect to a collection of TS Which are the most important periods to focus on? Which are the most important periods to focus on? The Distance Metric: Inter-Characteristics of TS G. Potamias, Institute of Computer Science, FORTH C. Dermon, Dept. of Biology, University of Crete NNESMED 2001 23/ 12

25 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 24/00 dist(Ts a, TS b ) The Distance Metric G. Potamias, Institute of Computer Science, FORTH C. Dermon, Dept. of Biology, University of Crete NNESMED 2001 24/ 12 Utilizing Statistical Significance If t a;i > t α/2 then the computed w a;i,i+1 is used otherwise the lowest weight for the respective change is used Control features adjustable and adaptive metric

26 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 25/00 Clustering: A Phylogeny-based Approach G. Potamias, Institute of Computer Science, FORTH C. Dermon, Dept. of Biology, University of Crete NNESMED 2001 25/ 12 TS-1 TS-4 TS-2 TS-5 TS-3 TS-6 Example: 1975 Micro-Sales, USA TS-1 TS-2 TS-5 TS-3 TS-4 TS-6 Phylogeny Trees: Informative Visualization

27 SETN 2002, April 11 2002, Thessaloniki, Greece -- George Potamias, ICS/FORTH Combined Distance & Feature-Based Clustering of Time-Series: An Application on Neurophysiology 26/00 Materials & Methods: In vivo autoradiographic method of 14 C-Leucine G. Potamias, Institute of Computer Science, FORTH C. Dermon, Dept. of Biology, University of Crete NNESMED 2001 26/ 12 14 C- Leucine Incorporation of 14 C-Leucine into protein Brain preparation 20μm thick cryosections Exposure to 14 C-sensitive film along with 14 C scale standards in dark room Development of autoradiographic film Image analysis fmoles/mg 240 120 2020 240 120 2020 fmoles/m g PA HVr


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