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Recently, the computer vision and machine learning community has been infavor of feature extraction pipelines that rely on a coding step followed by alinear classifier, due to their overall simplicity, well understood propertiesof linear classifiers, and their computational efficiency. In this paper wepropose a novel view of this pipeline based on kernel methods and Nystromsampling. In particular, we focus on the coding of a data point with a localrepresentation based on a dictionary with fewer elements than the number ofdata points, and view it as an approximation to the actual function that wouldcompute pair-wise similarity to all data points (often too many to compute inpractice), followed by a Nystrom sampling step to select a subset of all datapoints.  Furthermore, since bounds are known on the approximation power of Nystromsampling as a function of how many samples (i.e. dictionary size) we consider,we can derive bounds on the approximation of the exact (but expensive tocompute) kernel matrix, and use it as a proxy to predict accuracy as a functionof the dictionary size, which has been observed to increase but also tosaturate as we increase its size. This model may help explaining the positiveeffect of the codebook size and justifying the need to stack more layers (oftenreferred to as deep learning), as flat models empirically saturate as we addmore complexity.

Why Size Matters: Feature Coding as Nystrom Sampling