Abstract The autoencoder is an artificial neural network that performs nonlinear dimension reduction and learns hidden representations of unlabeled data. With a linear transfer function it is similar to the principal component analysis (PCA). While both methods use weight vectors for linear transformations, the autoencoder does not come with any indication similar to the eigenvalues in PCA that are paired with eigenvectors. We propose a novel autoencoder node saliency method that examines whether the features constructed by autoencoders exhibit properties related to known class labels. The supervised node saliency ranks the nodes based on their capability of performing a learning task. It is coupled with the normalized entropy difference (NED). We establish a property for NED values to verify classifying behaviors among the top ranked nodes. By applying our methods to real datasets, we demonstrate their ability to provide indications on the performing nodes and explain the learned tasks in autoencoders.
Studies have demonstrated the need to explain features in the latent space @cite_32 . For example, autoencoders have been applied on gnome-wide assays of cancer for knowledge extraction using their unsupervised nature @cite_43 @cite_16 . Cross validation is carried out on the latent representations of a denoising autoencoder with multiple activation thresholds. The result identifies the hidden nodes that give the best classification accuracy @cite_43 . In @cite_16 , variational autoencoders are built on the genomic data. A quick search for explanatory features are obtained by subtracting a series of mean values of latent representations. More insights are obtained by linking specific features to biological pathways.
@cite_43 @cite_16 @cite_32
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Big data bring new opportunities for methods that efficiently summarize and automatically extract knowledge from such compendia. While both supervised learning algorithms and unsupervised clustering algorithms have been successfully applied to biological data, they are either dependent on known biology or limited to discerning the most significant signals in the data. Here we present denoising autoencoders (DAs), which employ a data-defined learning objective independent of known biology, as a method to identify and extract complex patterns from genomic data. We evaluate the performance of DAs by applying them to a large collection of breast cancer gene expression data. Results show that DAs successfully construct features that contain both clinical and molecular information. There are features that represent tumor or normal samples, estrogen receptor (ER) status, and molecular subtypes. Features constructed by the autoencoder generalize to an independent dataset collected using a distinct experimental platform. By integrating data from ENCODE for feature interpretation, we discover a feature representing ER status through association with key transcription factors in breast cancer. We also identify a feature highly predictive of patient survival and it is enriched by FOXM1 signaling pathway. The features constructed by DAs are often bimodally distributed with one peak near zero and another near one, which facilitates discretization. In summary, we demonstrate that DAs effectively extract key biological principles from gene expression data and summarize them into constructed features with convenient properties. The Cancer Genome Atlas (TCGA) has profiled over 10,000 tumors across 33 different cancer-types for many genomic features, including gene expression levels. Gene expression measurements capture substantial information about the state of each tumor. Certain classes of deep neural network models are capable of learning a meaningful latent space. Such a latent space could be used to explore and generate hypothetical gene expression profiles under various types of molecular and genetic perturbation. For example, one might wish to use such a model to predict a tumor9s response to specific therapies or to characterize complex gene expression activations existing in differential proportions in different tumors. Variational autoencoders (VAEs) are a deep neural network approach capable of generating meaningful latent spaces for image and text data. In this work, we sought to determine the extent to which a VAE can be trained to model cancer gene expression, and whether or not such a VAE would capture biologically-relevant features. In the following report, we introduce a VAE trained on TCGA pan-cancer RNA-seq data, identify specific patterns in the VAE encoded features, and discuss potential merits of the approach. We name our method "Tybalt" after an instigative, cat-like character who sets a cascading chain of events in motion in Shakespeare9s "Romeo and Juliet." From a systems biology perspective, Tybalt could one day aid in cancer stratification or predict specific activated expression patterns that would result from genetic changes or treatment effects. Denoising autoencoders have been previously shown to be competitive alternatives to restricted Boltzmann machines for unsupervised pretraining of each layer of a deep architecture. We show that a simple denoising autoencoder training criterion is equivalent to matching the score (with respect to the data) of a specific energy-based model to that of a nonparametric Parzen density estimator of the data. This yields several useful insights. It defines a proper probabilistic model for the denoising autoencoder technique, which makes it in principle possible to sample from them or rank examples by their energy. It suggests a different way to apply score matching that is related to learning to denoise and does not require computing second derivatives. It justifies the use of tied weights between the encoder and decoder and suggests ways to extend the success of denoising autoencoders to a larger family of energy-based models.