Current Research Topic(s)
Homology
I'm currently working on the Big Data Visualization on top of distributed computing framework. Typically, the Computing Persistent Homology is of my interest visualizing algorithm, which defines a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
I'm currently working on the Big Data Visualization on top of distributed computing framework. Typically, the Computing Persistent Homology is of my interest visualizing algorithm, which defines a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
Past Research Topic(s)
Spatial Distance Histogram
I was working on particle simulation, which has become an important research technique in many scientific and engineering fields. Specifically, the 2-body correlation function (2-BCFs) is a statistical learning measurement in many research domains. One type of 2-BCF query called the Spatial Distance Histogram (SDH) is of vital importance in computational sciences. In a straightforward method, the SDH query takes quadratical running time. Dual-tree algorithms have been proposed to cut the running time of SDH computation. However, there are two different implementations of underlying data structures: quad-tree-based (oct-tree-based for 3-dimensional) and kd-tree-based data structure. Although it is easy to see that both implementations have the same time complexity, only require O(N^(2d-1/d)) running time to return the answer, where d is the number of dimensions of the dataset, a comparison of their actual running time under different scenarios have not been thoroughly studied. We presented a geometric modeling technique to quantitate the performance of dual-tree algorithms, and our qualitative analysis suggests, in 2D system, whenever the kd-tree-based implementation has one more level over quad-tree-based, the dual-tree algorithm would have nearly 25% speedup; in the 3D system, whenever the kd-tree-based implementation has one and two more level(s) over oct-tree-based, the speedup of dual-tree algorithm would have nearly 16% and 33%, respectively.
I was working on particle simulation, which has become an important research technique in many scientific and engineering fields. Specifically, the 2-body correlation function (2-BCFs) is a statistical learning measurement in many research domains. One type of 2-BCF query called the Spatial Distance Histogram (SDH) is of vital importance in computational sciences. In a straightforward method, the SDH query takes quadratical running time. Dual-tree algorithms have been proposed to cut the running time of SDH computation. However, there are two different implementations of underlying data structures: quad-tree-based (oct-tree-based for 3-dimensional) and kd-tree-based data structure. Although it is easy to see that both implementations have the same time complexity, only require O(N^(2d-1/d)) running time to return the answer, where d is the number of dimensions of the dataset, a comparison of their actual running time under different scenarios have not been thoroughly studied. We presented a geometric modeling technique to quantitate the performance of dual-tree algorithms, and our qualitative analysis suggests, in 2D system, whenever the kd-tree-based implementation has one more level over quad-tree-based, the dual-tree algorithm would have nearly 25% speedup; in the 3D system, whenever the kd-tree-based implementation has one and two more level(s) over oct-tree-based, the speedup of dual-tree algorithm would have nearly 16% and 33%, respectively.