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Multi-kernel learning has become a popular method to allow classification models greater flexibility in representing the relationships between data points. This approach has evolved into localized multi-kernel learning, which creates classification models that have the ability to adapt to a multi-scale feature-space. The advantages of such an approach are often hampered by additional parameters and hyper-parameters involved in creating this model, not to mention the greater likelihood of over-training. Additionally, existing methods to create a localized multi-kernel classifier rely on partitioning the feature-space, followed by applying a multi-kernel to the partitioned data points. We introduce a Bayesian approach to the localized multi-kernel machine. The new model is shown to provide greater classification abilities by learning the local scales of the feature-space without the need to partition the data. Also, the Bayesian formulation helps the model to be resistant to over-training. We demonstrate the models effectiveness on two landmine detection datasets, each from a different sensor type.