Abstract

Spatial clustering requires consideration of spatial information and this makes expectation-maximization (EM) algorithm that maximizes likelihood alone inappropriate. Although neighborhood EM (NEM) algorithm incorporates a spatial penalty term, it needs much more iterations for E-step. To incorporate spatial information while avoiding much additional computation, we propose a hybrid EM (HEM) approach that combines EM and NEM. Early training is performed via a selective hard EM till the penalized likelihood criterion begins to decrease. Then training is turned to NEM, which runs only one iteration of E-step and plays a role of finer tuning. Thus spatial information is incorporated throughout HEM and the computational complexity is also comparable to EM. Empirical results show that a few more passes are needed in HEM to converge after switching to NEM and the final clustering quality is close to or slightly better than standard NEM.

Keywords: Expectation-maximization algorithm; Spatial clustering; Gaussian mixture; Spatial penalty term

Article Outline

1. Introduction

1.1. Problem formulation

1.2. Related work

2. Basics of EM and NEM

2.1. Original EM

2.2. Entropy-based view

2.3. Neighborhood EM

2.3.1. Softmax function

3. Hybrid EM

3.1. Selective hardening

3.2. M-step implementation for fixing option

4. Experimental evaluation

4.1. Performance criteria

4.2. Satimage data

4.3. House price data

4.4. Bacteria image

5. Conclusion

References