Can we go the distance to predict how the brain represents the world? A distance-based partial least squares regression approach

How do we understand the world? One possible explanation would be that the brain semantically processes the perceptual information gathered from stimuli (e.g., objects, sounds). Researchers have tried to detect this semantic processing through various behavioral, neuroimaging and computational modeling approaches. A common feature of these approaches is the notion of distance, which quantifies the degree of similarity (or dissimilarity) between stimuli and has been used to represent behavioral and neural responses to these stimuli. One question that arises is: If the brain first responds to low-level (perceptual) information from the stimuli, can we detect the subsequent high-level (semantic) information that the brain imposes? To answer this question, we first need to know how the perceptual information is represented in the brain. Because we can use distances to represent the relationship between stimuli, an ideal solution is to predict the distance-based representation of the perceptual similarities between stimuli as encoded in the brain. Distances are traditionally analyzed with statistical methods such as Multidimensional Scaling (MDS), Generalized Procrustes Analysis (GPA), Individual Differences Scaling (INDSCAL), and DISTATIS, which represent distances as maps. MDS analyzes only one distance table at a time. GPA, INDSCAL and DISTATIS extract similarities between several distance tables. Our research question is related to prediction, but none of these methods are predictive. Partial Least Squares Regression (PLSR) is a method that can be used to predict a set of dependent variables (predictee) from a set of independent variables (predictor). However, PLSR does not analyze distances. Because no suitable methods exist to predict distances from distances, I have developed a new statistical method called Distance-based Partial Least Squares Regression (DISPLS). DISPLS adheres to a regression model and decomposes the predictee into prediction and error. I will use appropriate experimental data to show how DISPLS can model what the brain encodes as the sum of the low-level (perceptual) information predicted by stimuli and the high-level (semantic) information unique to the brain.