Chained regularization for identifying brain patterns specific to HIV infection

Abstract

Human Immunodeficiency Virus (HIV) infection continues to have major adverse public health and clinical consequences despite the effectiveness of combination Antiretroviral Therapy (cART) in reducing HIV viral load and improving immune function. As successfully treated individuals with HIV infection age, their cognition declines faster than reported for normal aging. This phenomenon underlines the importance of improving long-term care, which requires a better understanding of the impact of HIV on the brain. In this paper, automated identification of patients and brain regions affected by HIV infection are modeled as a classification problem, whose solution is determined in two steps within our proposed Chained-Regularization framework. The first step focuses on selecting the HIV pattern (i.e., the most informative constellation of brain region measurements for distinguishing HIV infected subjects from healthy controls) by constraining the search for the optimal parameter setting of the classifier via group sparsity (ℓ_2,1-norm). The second step improves classification accuracy by constraining the parameterization with respect to the selected measurements and the Euclidean regularization (ℓ₂-norm). When applied to the cortical and subcortical structural Magnetic Resonance Images (MRI) measurements of 65 controls and 65 HIV infected individuals, this approach is more accurate in distinguishing the two cohorts than more common models. Finally, the brain regions of the identified HIV pattern concur with the HIV literature that uses traditional group analysis models.

Keywords: Computational neuroscience; Group sparsity; Human immunodeficiency virus (HIV); MRI brain image analysis; Multiple kernel learning.

Figure A.9:

An illustration of computing the kernel for each pair of samples (x and x_n), similar to what is presented in Eq. (A.3). The final kernel is computed by a weighted aggregation of κ different kernels applied on each single feature.

Figure 1:

Training of the Chained-Regularization approach: The first step (top, denoted as Selection Step) selects the image measurements informative for distinguishing HIV from controls, while the second step (bottom, denoted as Reweighing Step) focuses on improving the accuracy by reweighing the selected measures for classifying the samples. Note, both steps are based on the same classifier but differ in regularizing (or constraining) its parameterization.

Figure 2:

Age distribution of the participants: HIV (left), Matched CTRL (middle), and CF CTRL (right).

Figure 3:

Illustration of feature grouping for group sparsity. (a) Regular sparsity (ℓ₁-norm) operates on a vector that concatenates the measurements from the left and right hemispheres. (b) Group sparsity operates on the matrix formed by putting the features from the same ROIs of the left and right hemispheres in its columns.

Figure 4:

Illustration of the nested cross-validation strategy used in Chained-Regularization (ℓ_2,1-ℓ₂-reg). On the i^th training iteration, the Selection Step selects the most informative measurements(i.e., the pattern) using ℓ_2,1-regularization, and then the Reweighing Step uses that pattern to build the classifier with ℓ₂-regularization. In the second step, inner cross-validation is used to choose the model hyperparameters. Next, the built classifier is used to calculate the accuracy scores on the corresponding testing fold (say Acci). The average accuracy for all folds is then reported (i.e., $\mathrm{Acc}=\frac{1}{10}{\sum }_{i=1}^{10}{\mathrm{Acc}}_i$).

Figure 5:

Frequencies of selection for each of the 298 features. Colors encode measurement types. The measurements in gray are those ignored in the Reweighing step.

Figure 6:

cortical ROIs selected by our proposed approach. (b-e) show the selected ROIs for each measurement type separately, while (a) visualizes the union of the four types.

Figure 7:

Subcortical ROIs and white matter structures selected by our method.

Figure 8:

Frequencies of selection for each of the measurement-subkernel pair. Note that 298 brain measurements are used, together with 7 different subkernels resulting in 2098 total pairs.