Spatial regularization based on support tensor machine for neuroimaging classification

2015 
Recently, a high dimensional classification framework has been proposed to introduce spatial and anatomical priors in support vector machine (SVM) optimization scheme for brain image analysis. However, classical SVM has to convert 3D discrete brain images naturally represented by higher-order tensors to one-dimensional vectors in order to meet the input requirements. This traditional method destroys the natural structure and correlation in the original data, and generates high dimensional vectors. In this manuscript, the method is improved by a modified support tensor machine (STM) algorithm to make full use of spatial prior and the inherent information of tensor. The new approach reduces memory requirements and computational complexity significantly, and it is comparably demonstrated by experimental results on classification of Alzheimer patients and elderly controls. Introduction Alzheimer disease (AD) is the most prevalent neurodegenerative dementia in worldwide, and thus prevention and early accurate diagnosis of AD is increasingly crucial. In the last few years, support vector machine (SVM) methods for AD subject classification have become an incredibly active research topic. In the related work, SVM approach, as same as feature selection and extraction, has been taking the specificity of neuroimaging data into account. As an example, a frame work is proposed in [1] to include spatial and anatomical priors into SVM by using regularization operators, and it indicates a flexible way to model various types of proximity. However, for the purpose of satisfying the input requirements of classical SVM, 3D discrete brain images naturally represented by higher-order tensors have to convert to vectors in advance. This conversion breaks the inherent structure and correlation in the original data, and easily produces high dimensional vectors and leads to a poor performance in time complexity and space complexity. In order to improve above method including spatial prior of 3D discrete brain images in SVM, a new method is proposed in this manuscript to maintain the natural structure in the original tensor data and include spatial prior of all frontal slices of the tensors in STM [2]. To illustrate the improvement, we apply the proposed method to classification of 299 subjects, 137 AD patients and 162 cognitively normal (CN) controls, as the same study population in [3]. It can be observed that the proposed method reduces size of memory requested and the time complexity significantly and produces better classification performances. Spatial prior in SVM SVM is a supervised learning algorithm introduced by Vapnik and performs classification by mapping the data into higher dimensional space [4]. Let (xs, ys), s∈1,...,S be a training set of instance-labeled pairs, xs∈Ω, ys∈{-1,1} and Ω is the input space, then SVM optimization problem can be written as:
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