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In many applications, machine learned (ML) models are required to hold some invariance qualities, such as rotation, size, intensity, and background invariance. Unlike many types of variance, the variants of background scenes cannot be ordered easily, which makes it difficult to analyze the robustness and biases of the models concerned. In this work, we present a technical solution for ordering background scenes according to their semantic proximity to a target image that contains a foreground object being tested. We make use of the results of object recognition as the semantic description of each image, and construct an ontology for storing knowledge about relationships among different objects using association analysis. This ontology enables (i) efficient and meaningful search for background scenes of different semantic distances to a target image, (ii) quantitative control of the distribution and sparsity of the sampled background scenes, and (iii) quality assurance using visual representations of invariance testing results (referred to as variance matrices). In this paper, we also report the training of an ML4ML assessor to evaluate the invariance quality of ML models automatically.