  Online real-estate information systems such as Zillow and Trulia have gained
increasing popularity in recent years. One important feature offered by these
systems is the online home price estimate through automated data-intensive
computation based on housing information and comparative market value analysis.
State-of-the-art approaches model house prices as a combination of a latent
land desirability surface and a regression from house features. However, by
using uniformly damping kernels, they are unable to handle irregularly shaped
regions or capture land value discontinuities within the same region due to the
existence of implicit sub-communities, which are common in real-world
scenarios. In this paper, we explore the novel application of recent advances
in spatial functional analysis to house price modeling and propose the
Hierarchical Spatial Functional Model (HSFM), which decomposes house values
into land desirability at both the global scale and hidden local scales as well
as the feature regression component. We propose statistical learning algorithms
based on finite-element spatial functional analysis and spatial constrained
clustering to train our model. Extensive evaluations based on housing data in a
major Canadian city show that our proposed approach can reduce the mean
relative house price estimation error down to 6.60%.
