Local image features can be assumed to be drawn from an unknown distribution. For image classification, such features are compared through the histogram-based model or the metric-based model. By quantizing these local features into a set of histograms, the histogram-based model is convenient and has vectorial representation of image but information could be lost in vector quantization. Unlike the histogram-based model, the metric-based model estimates the metrics over the underlying distribution of local features immediately, achieving better predictive performance. However, the model requires higher computational cost and loses the benefit of vectorial representation of image. To retain the advantages of these two models, this paper proposes the (doubly) randomized distribution features that represent the underlying distribution of local features in each image as a vectorial feature by utilizing random Fourier feature. We prove the convergences of the similarity and distance based on the randomized distribution feature. Remarkable advantages of the randomized distribution feature are that it has vectorial representation and thus computes efficiently as the histogram-based model. Besides, it provides rigorous theory guarantee and competitive performance as the metric-based model. Compared with several state-of-the-art algorithms, experiments in three real-world datasets justify that our proposed approaches attain competitive classification accuracy with faster computational speed. Furthermore, we indicate that our proposed features can utilize the methods in learning based on vectors, which are broadly studied in traditional machine learning domain, to deal with the problems in learning based on distribution.
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