A novel matrix-similarity based loss function for joint regression and classification in AD diagnosis

Abstract

Recent studies on AD/MCI diagnosis have shown that the tasks of identifying brain disease and predicting clinical scores are highly related to each other. Furthermore, it has been shown that feature selection with a manifold learning or a sparse model can handle the problems of high feature dimensionality and small sample size. However, the tasks of clinical score regression and clinical label classification were often conducted separately in the previous studies. Regarding the feature selection, to our best knowledge, most of the previous work considered a loss function defined as an element-wise difference between the target values and the predicted ones. In this paper, we consider the problems of joint regression and classification for AD/MCI diagnosis and propose a novel matrix-similarity based loss function that uses high-level information inherent in the target response matrix and imposes the information to be preserved in the predicted response matrix. The newly devised loss function is combined with a group lasso method for joint feature selection across tasks, i.e., predictions of clinical scores and a class label. In order to validate the effectiveness of the proposed method, we conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the newly devised loss function helped enhance the performances of both clinical score prediction and disease status identification, outperforming the state-of-the-art methods.

Keywords: Alzheimer's disease (AD); Feature selection; Joint sparse learning; Manifold learning; Mild Cognitive Impairment (MCI) conversion.

Figure 1

The framework of the proposed method.

Figure 2

An illustration of measuring matrix similarity by means of a graph matching. For simplicity, we showed only a small number of nodes. (a) Each node represents a column vector of the target or the predicted response matrix, edges represent the distance between nodes, and colors represent class labels. (b) Each node represents a row vector of the target or the predicted response matrix and edges denote the distance between nodes.

Figure 3

Comparison of classification ACCuracy (ACC) of the proposed method with single-task (“Single”) or multi-task (“Joint”) learning.

Figure 4

Receiver Operating Characteristic (ROC) curves for the proposed method using 4 different types of data.

Figure 5

Correlation Coefficients (CC) for ADAS-Cog (top) and MMSE (bottom) scores prediction with our method formulated for single-task (“Single”) or multi-task (“Joint”) regression.

Figure 6

Scatter plots and the respective Correlation Coefficients (CCs) obtained by the proposed method on MRI data (top: ADAS-Cog, bottom: MMSE).

Figure 7

Scatter plots and the respective Correlation Coefficients (CCs) obtained by the proposed method on PET data (top: ADAS-Cog, bottom: MMSE).

Figure 8

Scatter plots and the respective Correlation Coefficients (CCs) obtained by the proposed method on the MP data (top: ADAS-Cog, bottom: MMSE).

Figure 9

Scatter plots and the respective Correlation Coefficients (CCs) obtained by the proposed method on the MPC data (top: ADAS-Cog, bottom: MMSE).

Figure 10

Comparison of ACCuracy (ACC) (top), Correlation Coefficient (CC) of ADAS-Cog (middle), and CC of MMSE (bottom) among three graph based methods and also M3T.

Figure 11

Top 10 selected MRI/PET regions in the MCI classification with MPC. The brain regions were color-coded. Moreover, different colors indicate different brain regions.