Statistical methods for tissue array images - algorithmic scoring and co-training

Recent advances in tissue microarray technology have allowed immunohistochemistry to become a powerful medium-to-high throughput analysis tool, particularly for the validation of diagnostic and prognostic biomarkers. However, as study size grows, the manual evaluation of these assays becomes a prohibitive limitation; it vastly reduces throughput and greatly increases variability and expense. We propose an algorithm - Tissue Array Co-Occurrence Matrix Analysis (TACOMA) - for quantifying cellular phenotypes based on textural regularity summarized by local inter-pixel relationships. The algorithm can be easily trained for any staining pattern, is absent of sensitive tuning parameters and has the ability to report salient pixels in an image that contribute to its score. Pathologists' input via informative training patches is an important aspect of the algorithm that allows the training for any specific marker or cell type. With co-training, the error rate of TACOMA can be reduced substantially for a very small training sample (e.g., with size 30). We give theoretical insights into the success of co-training via thinning of the feature set in a high-dimensional setting when there is "sufficient" redundancy among the features. TACOMA is flexible, transparent and provides a scoring process that can be evaluated with clarity and confidence. In a study based on an estrogen receptor (ER) marker, we show that TACOMA is comparable to, or outperforms, pathologists' performance in terms of accuracy and repeatability.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS543 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

K-nearest Neighbor Search by Random Projection Forests

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we propose random projection forests (rpForests), for kNN search. rpForests finds kNNs by aggregating results from an ensemble of random projection trees with each constructed recursively through a series of carefully chosen random projections. rpForests achieves a remarkable accuracy in terms of fast decay in the missing rate of kNNs and that of discrepancy in the kNN distances. rpForests has a very low computational complexity. The ensemble nature of rpForests makes it easily run in parallel on multicore or clustered computers; the running time is expected to be nearly inversely proportional to the number of cores or machines. We give theoretical insights by showing the exponential decay of the probability that neighboring points would be separated by ensemble random projection trees when the ensemble size increases. Our theory can be used to refine the choice of random projections in the growth of trees, and experiments show that the effect is remarkable.Comment: 15 pages, 4 figures, 2018 IEEE Big Data Conferenc