Assistant Professor | Researcher in Optimization & Machine Learning
My research interests revolve around the development and application of mathematical optimization techniques to tackle critical challenges in high-dimensional contaminated data analysis. I am also drawn to problems related to clinical outcome prediction, treatment planning, medical imaging, and data-driven decision support systems. I firmly believe that the marriage of mathematics and biology holds the key to revolutionizing healthcare delivery and improving patient outcomes. My research agenda spans a broad range of research areas, including the extension of optimization theory, the design and implementation of algorithms, and the solution of biomedical problems.
Optimization: I have worked on designing and analyzing algorithms that are insensitive to outliers (unusual data) and demonstrating their usefulness in image and video analytics. Traditional algorithms and statistical procedures can lead, in the presence of outliers, to poor decisions. The new approaches are based on mathematical optimization. The new methods will be applied to the analysis of data that are known to contain outlier observations, such as biomedical data. I am also interested in the extension of kernel methods to machine learning algorithms and the associated preimage problem. Kernel methods over a mathematically elegant way to help extract the non-linear pattern in the data.
Precision oncology is defined as molecular profiling of tumors to identify targetable alterations, is rapidly developing, and has entered the mainstream of clinical practice. Imaging-guided multi-omics data-driven approaches are gaining significance in precision oncology. These approaches involve integrating data from various βomicsβ levels, such as genomics, proteomics, and transcriptomics, and combining them with advanced medical imaging techniques. This holistic approach provides a more comprehensive understanding of the molecular profile of the tumor and its spatial characteristics within the body. Clinicians and researchers should explore these emerging methodologies to improve the precision of diagnosis and treatment. In this context, part of my research plan will involve close collaboration with local medical centers to leverage clinical data and patient samples. This collaborative effort will utilize machine learning models to develop personalized cancer treatment modalities tailored to the unique molecular profiles and clinical characteristics of individual patients. Using the power of machine learning, my aim is to optimize treatment strategies for better patient outcomes. In addition, I am actively seeking funding opportunities from the National Institutes of Health (NIH) to support my ongoing research. Securing NIH funding will allow me to expand my research efforts, improve the scope of my studies, and accelerate the translation of innovative cancer treatment modalities into clinical practice.
Least Absolute Supervised PCA The least squares principal component analysis (LSPCA) is a gradientbased principal component regression. Unlike traditional principal component regression, LSPCA simultaneously finds an orthogonal subspace and fits a hyperplane of the ambient space of span(π , ππΏπ πΏ). One can argue that the πΏ1-norm regularization could provide this framework with robustness. One obtains straightforwardly as follows,
Extending LSPCA into high-dimensional feature space using kernel methods allows capturing non-linear patterns. My research explores different kernel techniques for optimal performance.