Detailed Instructions: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Problem:We introduce a new spatial data structure for high dimensional data called the approximate principal direction tree (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity to that of loweraccuracy RP trees. APD trees use a small number of powermethod iterations to find splitting planes for recursively partitioning the data. As such they provide a natural trade-off between the running-time and accuracy achieved by RP and PCA trees. Our theoretical results establish a) strong performance guarantees regardless of the convergence rate of the powermethod and b) that O(log d) iterations suffice to establish the guarantee of PCA trees when the intrinsic dimension is d. We demonstrate this trade-off and the efficacy of our data structure on both the CPU and GPU.
Solution:
Approximate Principal Direction Trees