Interactive Stream Surface Placement: A Hybrid Clustering Approach Supported by Tree Maps
Interactive Stream Surface Placement: A Hybrid Clustering Approach Supported By Tree Maps
Summary of Concept
A two-phase hybrid clustering algorithm with an in interactive tree map interface would be suitable to provide a visual overview and enable interactive selection of cluster details in structured and unstructured Computational Fluid Dynamics (CFD) data.
Contributions
The contributions of the paper are: -
- Improved computational speed and memory usage over recent vector field clustering work, resulting in the capability to efficiently process large, multi-dimensional datasets
- The creation of an algorithm to partition the flow field using k-means clustering, resulting in improved performance and allowing for researchers to overview the data based on pre-selected features.
- Creation of a technique to subdivide clusters based on Euclidean density, facilitating layered, hierarchical analysis and semi-automatic stream surface placement.
- A tree map interface to allow interactivity in selecting hierarchical clusters.
- Application of the techniques of visualization and interactivity to real world CFD data and validation of the method as the preferred option over similar ones by domain experts.
Related Work Summary
Clustering. Clustering algorithms can be divided into hierarchical clustering and partition-based clustering. The hierarchical approach, though providing a simplified representation of a vector field, is O (n2) complex, where n is the number of initial samples. This results in enhanced computational requirement. Partitioning algorithms such as k-means clustering are O (i.k.n) complex, where ‘k’ is the number of means and ‘I’ the number of iterations. Density Based Spatial Clustering of Applications with Noise (DBSCAN) is especially useful in partitioning a space based on local density. Our approach has combined the k-means clustering with the DBSCAN approach in a multi-layered format.
Tree Maps. Tree maps are useful in visualizing hierarchically structured information, mapping the entire hierarchy onto a rectangular area that can be shaded to improve perception. An improvement to the standard tree map representation is the ‘squarified tree’ where the rectangles approximate squares. This approach addresses the challenges of selecting and interacting with a large number of clusters in 3D space.
Summary of Implementation
The next step is the utilization of DBSCAN algorithm to further subdivide the clusters with an aim of partitioning all clusters with spatial separation in Euclidean space. Spatial separation is useful when examining the individual features in a flow field.
The third step is to build a hierarchical tree with k-means clusters as inner nodes and DBSCAN sub clusters as leaf nodes. This tree is then visualized with an interactive tree map, enabling the user to select any cluster or sub cluster. Squarified tree maps are used for the purpose. The resultant interactivity allows domain experts to focus selectively on the linked 3D flow.
Once a user selects the cluster of interest is selected, he is able to calculate the cluster’s spatial center, and the major and minor axis of covariance of the cluster’s second moments. These attributes are used to fit an oriented bounding box, called the seeding cuboid, to the cluster.
The fifth step is to compute the seeding curves at the cuboid boundary planes. Computing a scalar field representing the flow exit trajectory from the cuboid boundary helps achieve this task.
Summary of Results
In the field of computational fluid dynamics, domain experts crucially require tools to interact and explore the multi-dimensional data that becomes available. The clustering approach used by the researchers partitions the domain into meaningful subsets based on the fields of interest. Interaction with the clusters using a tree map is intuitive. Placement of stream surfaces at selected areas of interest provides feedback about the evolution of any attribute upstream or downstream. The researchers applied their technique to a real world simulation of a marine turbine. The visualization obtained in the marine turbine simulation used an array layout and demonstrated the efficacy of the model developed.
Analysis and Discussion
The evaluation of the work done by the researchers is best done when it is compared with recent work in the area. The algorithm compared favorably with hierarchical clustering. The bottleneck in the researchers’ model is the clustering parameter. The time for tree map generation is in the 7-65-millisecond range. Clustering and seeding attributes take 18-174 milliseconds to generate. Stream rendering by the researchers compares favorably to prior work on the subject. The memory usage is proportional to the size of the data set, as the researchers store only one integer per vertex to reference the corresponding cluster. Because the researchers use a hybrid clustering approach, their process is faster than the predecessor approach of pure hierarchical clustering by one order of magnitude. The inputs used by the model are the selection of the requisite data field, the number of centroids and a seeding cuboid isovalue. Thus, the model requires substantially simpler and lesser inputs than those required by prior models. The tree maps provide an invaluable flexibility to the domain engineers in the selection of individual clusters, as they can relate to the workflow visually and contextually. The model makes it easy for the domain engineer to derive the input and then visualize the precise features of interest. The model is successful in reinforcing the visual feedback through the contextual nature of clustering, making the environment intuitive for data exploration. Previous approaches, when applied to the marine turbine simulation, generated incomprehensible visualization. The proposed model has obviated this anomaly. The seeding curves enable localized exploration of the flow field.
Domain experts have appreciated the model. They have found the ability of the user to precisely isolate different regions of the domain and to evaluate them individually as an especially useful feature. They have also appreciated the flexibility provided by the tree map.
The model presented by the researchers thus significantly simplifies visualization of clusters in computational field dynamics using the least amount of computational power possible, and should prove to be a suitable aid for practical application by domain experts.
Reference
Edmunds, M., Laramee, R.S., Malki, R., Masters, I., Wang, Y., Chen, G., & Max, N. (n.d.). Interactive stream surface placement: A hybrid clustering approach supported by tree maps. Retrieved 13 Dec 2014, from http://cs.swansea.ac.uk/~csbob/research/seeding/surface/treemap/edmunds13interactive.pdf
