High-dimensional pattern regression using machine learning: from medical images to continuous clinical variables

Abstract

This paper presents a general methodology for high-dimensional pattern regression on medical images via machine learning techniques. Compared with pattern classification studies, pattern regression considers the problem of estimating continuous rather than categorical variables, and can be more challenging. It is also clinically important, since it can be used to estimate disease stage and predict clinical progression from images. In this work, adaptive regional feature extraction approach is used along with other common feature extraction methods, and feature selection technique is adopted to produce a small number of discriminative features for optimal regression performance. Then the Relevance Vector Machine (RVM) is used to build regression models based on selected features. To get stable regression models from limited training samples, a bagging framework is adopted to build ensemble basis regressors derived from multiple bootstrap training samples, and thus to alleviate the effects of outliers as well as facilitate the optimal model parameter selection. Finally, this regression scheme is tested on simulated data and real data via cross-validation. Experimental results demonstrate that this regression scheme achieves higher estimation accuracy and better generalizing ability than Support Vector Regression (SVR).

Figure 13

Regression results based on simulated data. Scatter plots of true scores vs. estimated scores by RVR / SVR, with four kinds of feature extraction methods: adaptive regional clustering, LDA, PCA and ISOMAP. The sloping black solid lines represent the regression lines.

Figure 1

A bagging framework of regression using RVM.

Figure 2

A sample with ten “follow-up” images in the simulated data.

Figure 3

MSEs for different kernel sizes of RVR based on regional features. The small graphs are correspond to different refined ranges of kernel sizes.

Figure 4

Most representative sections with regions of the group difference of the simulated data, as shown in the left figure. Parts R₁, R₂, and R₃ represent the areas of pathology, more details can be found in Section 3.1.

Figure 5

Scatter plots of clinically measured MMSE scores vs. estimated scores by RVR / SVR with four feature extraction methods: region clustering, LDA, PCA and ISOMAP. The graphs in the right column are for RVR, and those of the left column are for SVR. The sloping black solid lines represent the regression lines.

Figure 6

Scatter plots of clinically measured BNT scores vs. estimated scores by RVR based on four feature extraction methods.

Figure 7

Comparison of support / relevance vectors used in SVR and RVR. Curves show how the number of support/relevance vectors changes as the size of training samples increases.

Figure 8

GM, WM and CSF based regression results. Scatter plots of clinical measured MMSE vs. estimated MMSE by RVR / SVR with four feature extraction methods: regional clustering, LDA, PCA and ISOMAP. The two graphs in the first row show the best performance of RVR and SVR, respectively.

Figure 9

Histograms of MSEs and correlation coefficients for RVR with four different feature extraction methods performed on two information source: three tissues and GM only.

Figure 10

Clinically measured and estimated MMSE histograms by RVR with regional features from three tissues and GM, respectively.

Figure 11

MMSE change regression based on regional features.

Figure 12

Regions most representative of the group difference for different regression experiments based on ADNI data. (A: MMSE regression by using GM only; B: MMSE regression by using GM, WM and CSF; C: BNT regression by using GM; D: MMSE Change regression by using GM).