Traditional bidirectional two-dimension (2D) principal component analysis ((2D)PCA-L2) is sensitive to outliers because its objective function is the least squares criterion based on L2-norm. This paper proposes a simple but effective L1-norm-based bidirectional 2D principal component analysis ((2D)PCA-L1), which jointly takes advantage of the merits of bidirectional 2D subspace learning and L1...

Dowling et al. in 1 defined a norm in l1 which was used by Lin 2 to exhibit an equivalent norm which makes l1 into a space with the fixed point property FPP . A similar norm can be defined in every Banach spaceX with a basis. Since l1 with its usual norm does not have FPP, we asked ourselves if this norm in these spaces would also improve properties that imply the weak fixed point property WFPP...

for calculation of the displacements of points in micro geodesy networks, it is essential to discover stable and unstable points. without knowing stable points, calculated displacements are due to datum deficiency. in this case, calculated displacements are not valid. there are two methods to discover stable and unstable points: a-congruency robust method b- l1 norm minimization in this study t...

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The rec...

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LM...

The global localization methods deal with the estimation of the pose of a mobile robot assuming no prior state information about the pose and a complete a priori knowledge of the environment where the mobile robot is going to be localized. Most existing algorithms are based on the minimization of an L2-norm loss function. In spite of the extended use of the L2-norm, the use of the L1-norm offer...

in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...