Finding structure. Recovering evidence. Protecting meaning.

The problem

Real measurements arrive with far more dimensions than the process that generated them actually has. Isomap can recover that hidden low-dimensional shape, but it is slow on large datasets and a single bad neighbour link can fold the whole geometry in on itself.

The approach

Six connected papers attack the problem from different sides: a corrected neighbourhood graph, noise removal before the geometry is computed, A* search in place of exhaustive shortest paths, a divide-and-recombine scheme for scale, and Gaussian-process kernels for denoising that survives new data arriving.

Why it matters

Dimensionality reduction sits underneath visualization, clustering, and anomaly detection. When it distorts the geometry quietly, every conclusion drawn downstream inherits the distortion.

6 publications

The problem

Traffic sensors drop out — sometimes at random, sometimes in long correlated blocks when a whole corridor goes dark. Downstream forecasting treats the resulting gaps as if they were real, and degrades accordingly.

The approach

Treat the network as a tensor over location, direction, and time, and impose a compact multimode nonlinear transform on its nuclear norm, so that structure shared across all modes constrains the reconstruction. Recovery is driven by a convergent optimization strategy.

Why it matters

Signal timing, congestion pricing, and incident detection all consume this data directly. Gaps that go unrecovered become decisions made on evidence that is not there.

Publication

The problem

The datasets that would most repay analysis — clinical records above all — are the ones that cannot legally or ethically be centralized. Meanwhile the key management that protects them fails in known, specific ways.

The approach

Two strands. One examines where elliptic-curve cryptography holds and where it breaks in deployment. The other builds signcryption that addresses the key escrow and revocation problems directly, alongside federated approaches that move model updates instead of records.

Why it matters

Privacy-preserving analytics is what decides whether sensitive data gets used well or not at all. The guarantee has to be real, not procedural.

2 publications