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Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models
Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction—shared dimensionality and percent shared variance—with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure
Error Metrics for Learning Reliable Manifolds from Streaming Data
Spectral dimensionality reduction is frequently used to identify
low-dimensional structure in high-dimensional data. However, learning
manifolds, especially from the streaming data, is computationally and memory
expensive. In this paper, we argue that a stable manifold can be learned using
only a fraction of the stream, and the remaining stream can be mapped to the
manifold in a significantly less costly manner. Identifying the transition
point at which the manifold is stable is the key step. We present error metrics
that allow us to identify the transition point for a given stream by
quantitatively assessing the quality of a manifold learned using Isomap. We
further propose an efficient mapping algorithm, called S-Isomap, that can be
used to map new samples onto the stable manifold. We describe experiments on a
variety of data sets that show that the proposed approach is computationally
efficient without sacrificing accuracy
Diffusion Component Analysis: Unraveling Functional Topology in Biological Networks
Complex biological systems have been successfully modeled by biochemical and
genetic interaction networks, typically gathered from high-throughput (HTP)
data. These networks can be used to infer functional relationships between
genes or proteins. Using the intuition that the topological role of a gene in a
network relates to its biological function, local or diffusion based
"guilt-by-association" and graph-theoretic methods have had success in
inferring gene functions. Here we seek to improve function prediction by
integrating diffusion-based methods with a novel dimensionality reduction
technique to overcome the incomplete and noisy nature of network data. In this
paper, we introduce diffusion component analysis (DCA), a framework that plugs
in a diffusion model and learns a low-dimensional vector representation of each
node to encode the topological properties of a network. As a proof of concept,
we demonstrate DCA's substantial improvement over state-of-the-art
diffusion-based approaches in predicting protein function from molecular
interaction networks. Moreover, our DCA framework can integrate multiple
networks from heterogeneous sources, consisting of genomic information,
biochemical experiments and other resources, to even further improve function
prediction. Yet another layer of performance gain is achieved by integrating
the DCA framework with support vector machines that take our node vector
representations as features. Overall, our DCA framework provides a novel
representation of nodes in a network that can be used as a plug-in architecture
to other machine learning algorithms to decipher topological properties of and
obtain novel insights into interactomes.Comment: RECOMB 201
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