A Novel Discriminative Dictionary Pair Learning Constrained by Ordinal Locality for Mixed Frequency Data Classification

A dilemma faced by classification is that the data is not collected at the same frequency in some applications. We investigate the mixed frequency data in a new way and recognize them as a special style of multi-view data, in which each view data is collected at a different sampling frequency. This article proposes a discriminative dictionary pair learning method constrained by ordinal locality for mixed frequency data classification (shorted by DPLOL-MF). This method integrates synthesis dictionary and analysis dictionary into a dictionary pair, which not only improves computational cost caused by the ${\ell _0}$ or ${\ell _1}$-norm constraint, but also can deal with the sampling frequency inconsistency. The DPLOL-MF utilizes a synthesis dictionary to learn class-specified reconstruction information and employs an analysis dictionary to generate coding coefficients by analyzing samples. Particularly, the ordinal locality preserving term is leveraged to constrain the atoms of dictionaries pair to further facilitate the learned dictionary pair to be more discriminative. Besides, we design a specific classification scheme for the inconsistent sample size of mixed frequency data. This paper illustrates a novel idea to solve the classification task of mixed frequency data and the experimental results demonstrate the effectiveness of the proposed method.

1 Introduction

In real-world manufacturing applications, many important features (also called indicators or attributes) are not collected at the same frequency, though most machine learning methods assume that they are collected at the same frequency. For example, in the aluminum production process, the features such as electrolyte level, iron content and silicon content need to be acquired experimentally off-line. These features are low-frequency data. While the features such as working voltage, working current and vibration of the electrolytic cell can be uploaded in on-line through the sensors. These features are collected as high-frequency data.