Restricted Boltzmann Machines With Gaussian Visible Units Guided by Pairwise Constraints

Restricted Boltzmann machines (RBMs) and their variants are usually trained by contrastive divergence (CD) learning, but the training procedure is an unsupervised learning approach, without any guidances of the background knowledge. To enhance the expression ability of traditional RBMs, in this paper, we propose pairwise constraints (PCs) RBM with Gaussian visible units (pcGRBM) model, in which the learning procedure is guided by PCs and the process of encoding is conducted under these guidances. The PCs are encoded in hidden layer features of pcGRBM. Then, some pairwise hidden features of pcGRBM flock together and another part of them are separated by the guidances. In order to deal with real-valued data, the binary visible units are replaced by linear units with Gaussian noise in the pcGRBM model. In the learning process of pcGRBM, the PCs are iterated transitions between visible and hidden units during CD learning procedure. Then, the proposed model is inferred by approximative gradient descent method and the corresponding learning algorithm is designed. In order to compare the availability of pcGRBM and traditional RBMs with Gaussian visible units, the features of the pcGRBM and RBMs hidden layer are used as input "data" for K -means, spectral clustering (SP) and affinity propagation (AP) algorithms, respectively. We also use tenfold cross-validation strategy to train and test pcGRBM model to obtain more meaningful results with PCs which are derived from incremental sampling procedures. A thorough experimental evaluation is performed with 12 image datasets of Microsoft Research Asia Multimedia. The experimental results show that the clustering performance of K -means, SP, and AP algorithms based on pcGRBM model are significantly better than traditional RBMs. In addition, the pcGRBM model for clustering tasks shows better performance than some semi-supervised clustering algorithms.

Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity

Euclidean distance between instances is widely used to capture the manifold structure of data and for graph-based dimensionality reduction. However, in some circumstances, the basic Euclidean distance cannot accurately capture the similarity between instances; some instances from different classes but close to the decision boundary may be close to each other, which may mislead the graph-based dimensionality reduction and compromise the performance. To mitigate this issue, in this paper, we proposed an approach called Laplacian Eigenmaps based on Clustering-Adjusted Similarity (LE-CAS). LE-CAS first performs clustering on all instances to explore the global structure and discrimination of instances, and quantifies the similarity between cluster centers. Then, it adjusts the similarity between pairwise instances by multiplying the similarity between centers of clusters, which these two instances respectively belong to. In this way, if two instances are from different clusters, the similarity between them is reduced; otherwise, it is unchanged. Finally, LE-CAS performs graph-based dimensionality reduction (via Laplacian Eigenmaps) based on the adjusted similarity. We conducted comprehensive empirical studies on UCI datasets and show that LE-CAS not only has a better performance than other relevant comparing methods, but also is more robust to input parameters.

GRAPH MATCHING AND LEARNING IN PATTERN RECOGNITION IN THE LAST 10 YEARS

In this paper, we examine the main advances registered in the last ten years in Pattern Recognition methodologies based on graph matching and related techniques, analyzing more than 180 papers; the aim is to provide a systematic framework presenting the recent history and the current developments. This is made by introducing a categorization of graph-based techniques and reporting, for each class, the main contributions and the most outstanding research results.