Recently shape constrained classification has gained popularity in the machine learning literature order to exploit extra model information besides raw data features. In this paper, we present a new Lattice Linear Discriminant Analysis (Lattice-LDA) classifier, which allows take constraints of inputs, such as monotonicity and convexity/concavity. Lattice-LDA constructs nonparametric nonlinear d...

We describe use of Linear Discriminant Analysis (LDA) for data-driven automatic design of RASTA-like lters. The LDA applied to rather long segments of time trajectories of critical-band energies yields FIR lters to be applied to these time trajectories in the feature extraction module. Frequency responses of the rst three discriminant vectors are in principle consistent with the ad hoc designed...

An explicit global and unique isometric embedding into hyperbolic 3-space, H, of an axisymmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event hor...

In this paper we establish a duality between boosting and SVM, and use this to derive a novel discriminant dimensionality reduction algorithm. In particular, using the multiclass formulation of boosting and SVM we note that both use a combination of mapping and linear classification to maximize the multiclass margin. In SVM this is implemented using a pre-defined mapping (induced by the kernel)...

This paper proposes a locality correlation discriminant with neighborhood preserving embedding for face recognition, which considers both the locality correlation and manifold structure of the training data. A new locality correlation preserving within-class scatter matrix is defined, which not only contains the locality preserving information but also contains the neighbor correlation informat...

Recently, graph embedding has drawn great attention for dimensionality reduction in hyperspectral imagery. For example, locality preserving projection (LPP) utilizes typical Euclidean distance in a heat kernel to create an affinity matrix and projects the high-dimensional data into a lower-dimensional space. However, the Euclidean distance is not sufficiently correlated with intrinsic spectral ...

For supervised discriminant projection (SDP)method, the image matrix data are vectorized to find the intrinsic manifold structure, and the dimension of matrix data is usually very high, so SDP cannot be performed because of the singularity of scatter matrix. In addition, the matrix-to-vector transform procedure may cause the loss of some useful structural information embedding in the original i...

spectral-based subspace learning is a common data preprocessing step in many machine pipelines. The main aim to learn meaningful low dimensional embedding of the data. However, most methods do not take into consideration possible measurement inaccuracies or artifacts that can lead with high uncertainty. Thus, directly from raw be misleading and negatively impact accuracy. In this paper, we prop...

Recently graph based dimensionality reduction has received a lot of interests in many fields of information processing. Central to it is a graph structure which models the geometrical and discriminant structure of the data manifold. When label information is available, it is usually incorporated into the graph structure by modifying the weights between data points. In this paper, we propose a n...

Neighborhood Preserving Embedding (NPE) and extensions of NPE are hot research topics of data mining at present. An algorithm called Constraint Sparse Neighborhood Preserving Embedding (CSNPE) for dimensionality reduction is proposed in the paper. The algorithm firstly creates the local sparse reconstructive relation information of samples; then, exacts the pairwise constrain information of sam...