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In this work, sub-manifold projections based semi-supervised dimensionality reduction (DR) problem learning from partial constrained data is discussed. Two semi-supervised DR algorithms termed Marginal Semi-Supervised Sub-Manifold Projections (MS³MP) and orthogonal MS³MP (OMS³MP) are proposed. MS³MP in the singular case is also discussed. We also present(More)
This paper presents a two-dimensional Neighborhood Preserving Projection (2DNPP) for appearance-based face representation and recognition. 2DNPP enables us to directly use a feature input of 2D image matrices rather than 1D vectors. We use the same neighborhood weighting procedure that is involved in NPP to form the nearest neighbor affinity graph.(More)
Linear Discriminant Analysis (LDA) is a well-known dimensionality reduction algorithm for pattern recognition and machine learning. And Trace Ratio LDA (TR-LDA) and Null-space LDA (NLDA) are two popular variants of LDA. Both NLDA and TR-LDA can result in orthogonal transformations. However, they applied different schemes in deriving the optimal(More)
Dealing with high-dimensional data has always been a major problem in many pattern recognition and machine learning applications. Trace ratio criterion is a criterion that can be applicable to many dimensionality reduction methods as it directly reflects Euclidean distance between data points of within or between classes. In this paper, we analyze the trace(More)
Visualizing similarity data of different objects by exhibiting more separate organizations with local and multimodal characteristics preserved is important in multivariate data analysis. Laplacian Eigenmaps (LAE) and Locally Linear Embedding (LLE) aim at preserving the embeddings of all similarity pairs in the close vicinity of the reduced output space, but(More)
Isomap is a well-known nonlinear dimensionality reduction (DR) method, aiming at preserving geodesic distances of all similarity pairs for delivering highly nonlinear manifolds. Isomap is efficient in visualizing synthetic data sets, but it usually delivers unsatisfactory results in benchmark cases. This paper incorporates the pairwise constraints into(More)
—Bearings are critical components in induction motors and brushless direct current motors. Bearing failure is the most common failure mode in these motors. By implementing health monitoring and fault diagnosis of bearings, unscheduled maintenance and economic losses caused by bearing failures can be avoided. This paper introduces trace ratio linear(More)
This paper incorporates the group sparse representation into the well-known canonical correlation analysis (CCA) framework and proposes a novel discriminant feature extraction technique named group sparse canonical correlation analysis (GSCCA). GSCCA uses two sets of variables and aims at preserving the group sparse (GS) characteristics of data within each(More)
Dealing with high-dimensional data has always been a major problem in research of pattern recognition and machine learning, and Linear Discriminant Analysis (LDA) is one of the most popular methods for dimension reduction. However, it only uses labeled samples while neglecting unlabeled samples, which are abundant and can be easily obtained in the real(More)