Novel Event Signature Detection

Novel Event Signature Detection encompasses the discovery, analysis, and interpretation of underlying patterns and information signatures within complex data structures. Our first two method was discussed already in section DeblurSR and Learning Transferable Cloaks. Two additional cutting-edge methodologies are at the forefront of current research: Higher Order Feature Selection (HOFS) and Probabilistic PolarGMM. These methods, outlined below, exemplify advancements in feature selection, unsupervised clustering, and noisy projection image analysis.

The novel contributions in event signature detection showcase the continuous innovation in the realms of feature selection and unsupervised learning. By advancing mutual information approximation techniques and unsupervised clustering methods, the highlighted research propels the understanding of complex patterns within data. The extension of traditional methodologies to higher-order constructs and probabilistic models marks a significant progression in the field, broadening the horizons for future exploration and application. These advancements not only serve to enrich the current landscape of data analytics but also pave the way for more sophisticated and nuanced analyses in various domains.

HOFS: Higher Order Mutual Information Approximation for Feature Selection in R

Feature selection is a pivotal step in predictive modeling, where relevant features must be identified to enhance model quality (Gajowniczek et al., 2022). HOFS presents a novel approach to this task, utilizing higher-order mutual information (MI) approximation. Contrary to existing methods, which often lead to locally optimal selections:

1. Higher Order Approximation: HOFS employs a higher order MI-based technique, bypassing the limitations of the traditional lower order approximation.

2. Ranked Collection: Instead of a single list, HOFS provides a ranked collection of feature subsets that maximizes MI, thereby acknowledging interdependent features.

3. Performance Excellence: The proposed method outshines existing feature selection approaches, maintaining similar running times and computational complexity while delivering more nuanced feature ranking.

This methodology extends the boundaries of feature selection, allowing for the identification of non-local feature combinations and fostering a deeper understanding of their interdependence.

Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy Projection Images of Unknown Pose

In the domain of cryogenic electron microscopy (Cryo-EM), unsupervised clustering and alignment play a significant role in inferring orientations and grouping similar images (Chockchowwat & Bajaj, 2022). The Probabilistic PolarGMM methodology introduces:

1. Fourier-Bessel Steerable PCA: An efficient, adaptable, low-rank rotation operator, extended to handle translations, serves as the foundational representation.

2. Unsupervised Learning: Utilizing a probabilistic polar-coordinate Gaussian mixture model, soft clusters are learned through an expectation-maximization (EM) algorithm.

3. Robust Alignment: The method exhibits robustness against alignment imperfections, enhancing the reliability of rotational clusters.

Multiple benchmarks demonstrate the superiority of probabilistic PolarGMM against standard Cryo-EM tools in various clustering metrics and alignment errors, affirming its potential for improved performance in very noisy projection image analysis. The pipeline is shown in figure 1 and some results are shown in figure 2.

References

• Gajowniczek, K., Wu, J., Gupta, S., & Bajaj, C. (2022). HOFS: Higher order mutual information approximation for feature selection in R. SoftwareX, 19, 101148.

• Chockchowwat, S., & Bajaj, C. L. (2022). Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy Projection Images of Unknown Pose. ArXiv Preprint ArXiv:2206.12959.