In this paper, we present a new dimensionality reduction (DR) method (SSGEAL) which integrates Graph Embedding (GE) with semi-supervised and active learning to provide a low dimensional data representation that allows for better class separation. Unsupervised DR methods such as Principal Component Analysis and GE have previously been applied to the classification of high dimensional biomedical datasets (e.g. DNA microarrays and digitized histopathology) in the reduced dimensional space. However, these methods do not incorporate class label information, often leading to embeddings with significant overlap between the data classes. Semi-supervised dimensionality reduction (SSDR) methods have recently been proposed which utilize both labeled and un-labeled instances for learning the optimal low dimensional embedding. However, in several problems involving biomedical data, obtaining class labels may be difficult and/or expensive. SSGEAL utilizes labels-from instances, identified as "hard to classify" by a support vector machine based active learning algorithm, to drive an updated SSDR scheme while reducing labeling cost. Real world biomedical data from 7 gene expression studies and 3900 digitized images of prostate cancer needle biopsies were used to show the superior performance of SSGEAL compared to both GE and SSAGE (a recently popular SSDR method) in terms of both the Silhouette Index (SI) (SI = 0.35 for GE, SI = 0.31 for SSAGE, and SI = 0.50 for SSGEAL) and the Area Under the Receiver Operating Characteristic Curve (AUC) for a Random Forest classifier (AUC = 0.85 for GE, AUC = 0.93 for SSAGE, AUC = 0.94 for SSGEAL).
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