An empirical comparison of four initialization methods for the K-Means algorithm
Pattern Recognition Letters
A Unified Approach to Detecting Spatial Outliers
Geoinformatica
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Many spatial data mining and spatial modeling approaches use Euclidean distance in modeling spatial dependence. Although meaningful and convenient, Euclidean distance has weaknesses. These include providing an over simplified representation of spatial dependence, being limited to certain spatial pattern and symmetrical relationships, being unable to account for cross-class dependencies, and unable to work with categorical especially multinomial data. This paper introduces Hidden Markov Model (HMM) as an attractive approach to uncovering hidden spatial patterns. The HMM assumes that a hidden state (factor or process) generates observable symbols (indicators). This doubly embedded stochastic approach uncovers hidden states based on observed symbol sequences using two integrated sets of probabilities, transition probability and emission probability. As an alternative to Euclidean distance based approaches, the HMM measures spatial dependency by transition probabilities and cross-class correlation better capturing geographic context. HMM works with data of any measurement scale and dimension. To demonstrate the method, we assume urban spatial structure as a hidden spatial factor underlying single family housing unit prices in Milwaukee, Wisconsin, we then use the HMM to uncover four hidden spatial states from home sale prices.