Within the framework, how to encode each local feature has significant impact on the final classification performance. The traditional and the simplest coding method is Vector Quantization (VQ) [12] (a.k.a. Hard Quantization or Hard Assignment), which assigns a local feature to the closest visual word in the codebook/vocabulary, introducing unrecoverable discriminative information loss. The Soft Assignment (SA) coding method [14-16] is proposed to reduce information loss by assigning a local feature to different visual words according to its memberships to multiple visual words. Apart from information loss, traditional SPM based on VQ has to use a classifier with nonlinear Mercer kernels, resulting in additional computational complexity and reducing scalability for real application. To alleviate these limitations, Sparse Coding based SPM (ScSPM) [1], Local Coordinate Coding (LCC) [11] and Locality-constrained Linear Coding (LLC) [2] aims at obtaining a nonlinear feature representation which works better with linear classifiers. They search for some weighted coefficients to linearly combine visual words of the codebook to approximate the input low-level descriptor. Salient Coding (SaC) [17] and its extension Group Salient Coding (GSC) [18] is proposed to speed-up while reserving the classification accuracy.

Here, we introduce three kinds of coding schemes, i.e., VQ, SA, its extension Localized Soft-assignment Coding (LSC) and LLC. Let X = {xi, x2,..., xN} e RDxN be a set of local descriptors extracted from an image, where D is the descriptor dimensionality and N is the total number of descriptors. Given a codebook with M entities (a.k.a. visual words, atoms), i.e., B = {b1; b2,..., bM} e RDxM, then the corresponding codes of an image Y = {y1; y2,...,yN} e RMxN can be generated by using various coding schemes.

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