The goal of this article is to develop a pattern recognition algorithm for detecting periods of food intake based on passively collected wearable device motion sensor data, accelerometer and gyroscope in a free-living condition. The main contributions of this work are the following. First, we use recently developed methods in topological data analysis (TDA) to create and extract key features. Second, we employ a novel Bayesian feature selection tool, BVSNLP, to reduce the dimensionality of the problem. Developing this algorithm in an efficient way, we believe it can be deployed on edge devices as well. We demonstrate the performance of our method on a dataset that contains a total of 1000 hours of accelerometer and gyroscope sensor data from 13 subjects.