Patch distribution compatible semisupervised dimension reduction for face and human gait recognition

We propose a new semisupervised learning algorithm, referred to as patch distribution compatible semisupervised dimension reduction, for face and human gait recognition. Each image (a face image or an average human silhouette image) is first represented as a set of local patch features and it is further characterized as the corresponding patch distribution feature, which can be expressed as an image-specific Gaussian mixture model (GMM) adapted from the universal background model. Assuming that the individual components of the image-specific GMMs from all the training images reside on a submanifold, we assign a component-level prediction label matrix F ^k to each individual GMM component and introduce a new regularizer based on a set of local submanifold smoothness assumptions in our objective function. We also constrain each component-level prediction label matrix F ^k to be consistent with the image-level prediction label matrix F, as well as enforce F to be close to the given labels for the labeled samples. We further use a linear regression function h(X)=X ^TW+1b ^T to provide embeddings for the training data and the unseen test data. Inspired by the recent work flexible manifold embedding, we additionally integrate the regression residue ∥h(X)-F∥ ² in our objective function to measure the mismatch between h(X) and F, such that our method can better cope with the data sampled from a nonlinear manifold. Finally, the optimal solutions of the component-level prediction label matrix F ^k, the image-level prediction label matrix F, the projection matrix W, and the bias term b can be simultaneously obtained. Comprehensive experiments on three benchmark face databases CMU PIE, FERET, and AR as well as the USF HumanID gait database clearly demonstrate the effectiveness of our algorithm over other state-of-the-art semisupervised dimension reduction methods.