#analyticsx Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton North Carolina State University ABSTRACT METHODS HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY • We propose a hierarchical activity clustering methodology, which incorporates the use of topological persistence analysis, to capture the hierarchies present in the data. • The key innovations presented in this research include the hierarchical characterization of the activities over a temporal parameter as well as the characterization and parameter selection based on stability of the results using persistence analysis. RESULTS CONCLUSION & FUTURE WORK . • We show how persistence diagrams can help reduce computation time and help choose stable models for our hierarchical representations. Furthermore, we are able to characterize the stability of our results via persistence analysis. • Our future work will involve testing our method on other datasets and comparing it with other existing algorithm. Aggregated Persistence Diagrams • Regions in the diagram corresponding to the three values of ϵ that produce the most robust graphical models are shown in (d), (e) and (f). • The selected models will not change if ϵ is perturbed within the specified ranges. These ranges are also highlighted as pink regions in the diagram. Assumptions: • Let () be the sensor observations at time . • Let , : 0, →ℝ be sensor observation trajectories over , +. That is, , ≔ ( + ) • We define a dissimilarity metric ( 1 , , 2 , ) and construct point clouds as in Fig.1 Approach: • We perform a filtration of the space for each by using the dissimilarity metric for a fixed . • A multi-scale representation is obtained by considering the structure of the data over . • Persistence homology allows us to keep a record of which clusters persist as shown in Fig.2. DATASET Results & Analysis • Classification results shown in Fig.5, show the average class accuracy. • Picking a small τ (i.e., the size of the data window) and a large enough ϵ (i.e., the clustering radius) gives us a better classification accuracy. • The models are stable over the bound specified in the diagrams in Fig. 4. Protocol Training • Hierarchical clustering is performed using the point clouds for each value of as the clustering parameter ϵ is increased. • Regions with higher densities are clustered into a single cluster and labeling was performed by using the majority vote rule. • Fig 3 shows a video of the training scheme over different values of τ. Data stream Video Fig. 1 Fig. 2 Fig. 4 Fig. 3 Fig. 5 Training video
Transcript
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Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
North Carolina State University
ABSTRACT
METHODS
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
• We propose a hierarchical activity clustering methodology, which incorporates the use of topological
persistence analysis, to capture the hierarchies present in the data.
• The key innovations presented in this research include the hierarchical characterization of the activities over a
temporal parameter as well as the characterization and parameter selection based on stability of the results
using persistence analysis.
RESULTS
CONCLUSION & FUTURE WORK.
• We show how persistence diagrams can help reduce computation time and help choose stable models for our
hierarchical representations. Furthermore, we are able to characterize the stability of our results via persistence
analysis.
• Our future work will involve testing our method on other datasets and comparing it with other existing algorithm.
Aggregated Persistence Diagrams• Regions in the diagram corresponding to the three values of ϵ that
produce the most robust graphical models are shown in (d), (e)
and (f).• The selected models will not change if ϵ is perturbed within the
specified ranges. These ranges are also highlighted as pink
regions in the diagram.
Assumptions:
• Let 𝑥(𝑡) be the sensor observations at time 𝑡.• Let 𝛾𝑘,𝜏: 0, 𝜏 → ℝ𝑁 be sensor observation trajectories over 𝑡𝑘, 𝑡𝑘 + 𝜏 .
That is, 𝛾𝑘,𝜏 𝑡 ≔ 𝑥(𝑡 + 𝑡𝑘)
• We define a dissimilarity metric 𝐷(𝛾𝑘1,𝜏, 𝛾𝑘2,𝜏) and construct
point clouds as in Fig.1
Approach:
• We perform a filtration of the space for each by using the dissimilarity
metric for a fixed 𝜏.
• A multi-scale representation is obtained by considering the structure of
the data over 𝜏.
• Persistence homology allows us to keep a record of which clusters
persist as shown in Fig.2.
DATASET
Results & Analysis
• Classification results shown in Fig.5, show the average class
accuracy.
• Picking a small τ (i.e., the size of the data window) and a large
enough ϵ (i.e., the clustering radius) gives us a better classification
accuracy.
• The models are stable over the bound specified in the diagrams in
Fig. 4.
Protocol
Training
• Hierarchical clustering is performed using the point clouds for each value of 𝜏 as the clustering parameter ϵ is increased.
• Regions with higher densities are clustered into a single cluster and labeling
was performed by using the majority vote rule.
• Fig 3 shows a video of the training scheme over different values of τ.
Data stream Video
Fig. 1
Fig. 2
Fig. 4
Fig. 3
Fig. 5
Training video
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DATASET
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
North Carolina State University
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
Mocap generated skeleton Joint Position Acceleration ECG + HR
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HIERARCHICAL STRUCTURE OVER THE TRAINING SET
τ
0
40
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
North Carolina State University
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
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North Carolina State University
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
A filtration of a set of points based on a specified metric (left) and its
corresponding persistence diagram (right). Note that two connected components
are born at ϵ (shown in blue in the persistence diagram), one of which
disappears at ϵ2. A single hole (shown in red in the persistence diagram)
appears at ϵ2 and disappears at ϵ4
Constructing a point cloud from the data streams. Motion trajectories and corresponding
activity labels corresponding to the x-coordinates of the left wrist and right ankle of an
individual (left). Projections of the point cloud and the activity labels for different values of τ
(right)
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North Carolina State University
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
Average performance accuracy for each class
Aggregated Persistence Diagrams. The points in the persistence diagrams shown in (a), (b)
and (c) correspond to the connected components for all levels of τ. Regions in the diagram corresponding to the three values of ϵ that produce the most robust graphical models are
shown in (d), (e) and (f). The selected models will not change if ϵ is perturbed within the
specified ranges.
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North Carolina State University
HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
REFERENCES
• Lara, O.D. and Labrador, M.A., 2013. A survey on human activity recognition using wearable sensors. IEEE
