Application of Power K Means for Multiview Data | Master’s Final Year Project

Formulated a novel clustering framework - Cluster Weighted Kernel Power K Means extending Multiview Kernel Power K-Means to optimize non-convex objective functions and mitigate local minima limits.

  • Framework: Kernelized data projections via Reproducing Kernel Hilbert Space (RKHS).
  • Optimization: Solved non-convexity constraints utilizing the Majorization-Minimization (MM) algorithm to dynamically weight inner clusters across multiple views.
  • Benchmarks: Validated clustering accuracy on simulated frameworks and Caltech 101 dataset using NMI and ARI metrics.

Project Link

Stochastic Modeling of Ecological Systems: Beyond Lotka-Volterra

  • Objective: Model predator-prey population dynamics by transitioning from rigid deterministic frameworks to stochastic biological systems, accounting for conservation-driven resource injections.
  • Methodology & Theory:
    • Introduced stochastic perturbations into the classic Lotka-Volterra differential equations to derive conditions for long-term population equilibrium versus systemic extinction.
    • Addressed the structural limitations of Lotka-Volterra (which assumes isolated ecosystems) by fitting a non-linear Rosenzweig-MacArthur model. This integrated external resource variables (additional food supplied to stabilize the ecosystem).
  • Simulation & Analytics: Conducted comprehensive time-series simulation studies to evaluate predator-prey frequencies over time, mapping out phase portraits and bifurcation behaviors across varied birth, death, and supplemental feeding rates.

Project Link

Clinical Data Analysis: Dietary Impacts on CKD-Induced Constipation

  • Objective: Investigate the causal relationship between dietary habits and secondary constipation in patients suffering from Chronic Kidney Disease (CKD).
  • Statistical Methodology:
    • Evaluated initial baselines using linear regression across ordinal survey responses, applying Box-Cox transformations and Quantile-Quantile ($Q\text{-}Q$) plots to address non-normality.
    • Advanced the architecture by fitting an Ordinal Logistic Regression Model to properly treat the discrete, ordered nature of the response variables.
    • Executed hyperparameter tuning to mitigate overfitting, verified structural integrity via Variance Inflation Factor ($VIF$) to rule out multicollinearity, and maximized the adjusted $R^2$.
  • Impact: The validated statistical insights and risk factors were directly utilized by clinical nephrologist to establish dietary causality guidelines for CKD patient care.

Project Link

Predictive Modeling: US Healthcare Insurance Cost Dynamics

  • Objective: Construct a predictive pipeline to estimate healthcare insurance premiums across diverse demographic profiles.
  • Statistical Methodology:
    • Executed rigorous Exploratory Data Analysis (EDA) using stratified boxplots and scatter matrices to map multi-variable correlations (Age, BMI, Sex, Region, Offspring count).
    • Evaluated initial baselines with a Linear Regression model, identifying high predictive accuracy for the smoker cohort but severe heteroscedasticity and outlier density within the non-smoker cohort.
    • Pivoted to a non-parametric $K$-Nearest Neighbor (KNN) framework to better capture non-linear interactions and structural anomalies without distributional assumptions.
  • Optimization: Employed $k$-fold cross-validation to algorithmically determine the optimal hyperparameter value for $K$, minimizing root-mean-square error (RMSE).