Sorting Five Human Tumor Types Reveals Specific Biomarkers and Background Classification Genes.

We applied two state-of-the-art, knowledge independent data-mining methods - Dynamic Quantum Clustering (DQC) and t-Distributed Stochastic Neighbor Embedding (t-SNE) - to data from The Cancer Genome Atlas (TCGA). We showed that the RNA expression patterns for a mixture of 2,016 samples from five tumor types can sort the tumors into groups enriched for relevant annotations including tumor type, gender, tumor stage, and ethnicity. DQC feature selection analysis discovered 48 core biomarker transcripts that clustered tumors by tumor type.

Reducing memory cost of exact diagonalization using singular value decomposition.

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, without restricting to variational ansatzes. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of n(svd) smaller subcluster vectors using singular value decomposition.

Dynamic quantum clustering: a method for visual exploration of structures in data.

A given set of data points in some feature space may be associated with a Schrödinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrödinger equation.