Multilinear maximum distance embedding via L₁-norm optimization

Dimensionality reduction plays an important role in many machine learning and pattern recognition tasks. In this paper, we present a novel dimensionality reduction algorithm called multilinear maximum distance embedding (M ²DE), which includes three key components. To preserve the local geometry and discriminant information in the embedded space, M²DE utilizes a new objective function, which aims to maximize the distances between some particular pairs of data points, such as the distances between nearby points and the distances between data points from different classes. To make the mapping of new data points straightforward, and more importantly, to keep the natural tensor structure of high-order data, M²DE integrates multilinear techniques to learn the transformation matrices sequentially. To provide reasonable and stable embedding results, M²DE employs the Li-norm, which is more robust to outliers, to measure the dissimilarity between data points. Experiments on various datasets demonstrate that M²DE achieves good embedding results of high-order data for classification tasks.