Abstract
Discriminant analysis is an important tool in machine learning. One of the motivations of this paper is to judge whether a dataset is suitable for discriminant analysis. At present, tensor data are becoming more and more popular in machine learning. Another motivation is to propose a dimensionality reduction algorithm of tensor data which facilitates discriminant analysis of tensor data. The first contribution of this paper is to propose a criterion to measure the potential ability of discriminant analysis of a dataset, and the criterion is called Maximum Discriminant Difference (MDD). The second contribution is to propose a dimensionality reduction algorithm of tensor data based on the mode product of tensor and MDD, called MDD-TDR for short. The first innovation of this paper is that, although MDD is inspired by Linear discriminant analysis (LDA), MDD is a criterion, not an algorithm. MDD can be applied to many applications, not just dimensionality reduction. Furthermore, MDD can be applied to both supervised and unsupervised learning. The second innovation is that, unlike many other tenor dimensionality reduction algorithms that are linear and align tenor into a vector for processing, MDD-TDR is nonlinear and iterative, and in each iteration, each dimension of a tensor is dimensionally reduced separately. The experimental results on 5 widely-used landmark datasets show MDD-TDR outperforms 7 related algorithms published in top academic journals in recent years.
Highlights
As people deepen their understanding of things, there are more and more dimensions to depict things, which leads to the popularity of multidimensional data
Maximum Discriminant Difference (MDD) is inspired by Linear discriminant analysis (LDA), MDD is a criterion, not an algorithm of dimensionality reduction
MDD ( ) is a criterion while LDA is an algorithm of dimensionality reduction, and MDD ( ) can have many different applications in machine learning
Summary
As people deepen their understanding of things, there are more and more dimensions to depict things, which leads to the popularity of multidimensional data. In real-world applications, some dimensions of the multidimensional data are often very high. The calculation of high-dimensional data usually requires a lot of computing resources, so the research on dimensionality reduction algorithms for high-dimensional data is very necessary. Dimensionality reduction algorithms have been widely used in many fields of video recognition [1], face recognition [2], object detection [3], and highhyperspectral images [4]. The dimensionality reduction algorithms can be divided into two kinds. The first kind refers to linear dimensionality reduction methods, which directly project high-dimensional space into low-dimensional space. The linear dimensionality reduction methods cannot reduce the dimensionality of the nonlinear-structured data. Nonlinear dimensionality reduction algorithms have received wide attention
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