43 Detecting Nonsynchronous Heart Cells from Video – An Unsupervised Machine Learning Approach 419 Fig. 43.3 Methodology 43.4.1 Non-negative Matrix Factorization on Videos AV matrix of dimensions n ×mwas first constructed from the data for each video with n rows containing pixel intensities for mnumber of pixels. Matrix V was then decomposed into two approximated matrices, Wand H, using a least squares approximation. Matrix Wcontains r observations that can be reconstructed into a new video using the weights of matrix H. Several values for rankr ranging between 2 and 60 were tested. The greater the rank, the more likely that local motion would be captured in some of the components. Signals from the weight matrix, H, were plotted to identify potential anomalies. Comparing Fig. 43.4 with Fig. 43.5, it is difficult to say whether a specific component corresponds to a nonsynchronous heart cell. However, observing and comparing peak patterns can narrow down the components to focus on. All ten components in Fig. 43.4 share similar patterns, which allude to the global motion of heart cells. Multiplying the extracted features, W, by its corresponding coefficients matrix, H, gives a video reconstruction containing only the signal from that individual component. When attempting to reconstruct Video A with the same ten components, the local motion was completely removed. On the other hand, Fig. 43.5 has several distinct components (i.e. components 20, 22, and 29), of which one may correspond to a nonsynchronous heart cell. Reconstructing all 30 components resulted in a new video that was similar to the original. Since it is often challenging to isolate the local motion by reconstructing a new video with hand-selected components, a different approach to visualize cell motion for each component from non-negative matrix factorization is proposed. Instead of analyzing the weight matrix, H, to output signals for each component, we can focus on the spatial matrix, W, to produce images with scaled colors that are a measure of pixel contribution. As expected from Fig. 43.6, approximately the first half of the components correspond to global motion since most of the cardiac myocytes are present. Additionally, nonsynchronous heart cells are found in component 22 (Fig. 43.7). In Video A, since the nonsynchronous heart cell on the right is beating more profoundly than the one of the left, non-negative matrix factorization generates a more defined structure for that cell. For videos with multiple cells beating at various frequencies, they are more likely to be scattered across multiple components. If a nonsynchronous heart cell is larger in size relative to the other cells in the videos, then its discrete motion can be perceived more clearly in the image with scaled colors. On the contrary, if the nonsynchronous heart cell is faint within the image, then it is suggested for visualization purposes to crop the video and rerun the program. Doing so magnifies the local motion at a greater scale, which in turn, enhances the features of the anomaly. A consequence to using non-negative matrix factorization is that the algorithm is stochastic, meaning that the components – signals and images – created are always random each time the program is run. Depending on the number of components, the outputs will not consistently capture the anomalies. Moreover, there are tradeoffs when choosing the rank. Performing non-negative matrix factorization with a large rank yields more sensitive components that may likely capture the nonsynchronous heart cells; however, running the program for higher rank will require more computational resources. While this method has some success in pinpointing the exact location of the nonsynchronous heart cells, the next step is to reconstruct the video to isolate local motion.
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