Analyzing and clustering neural data

This thesis aims to analyze neural data in an overall effort by the Charles Stark Draper Laboratory to determine an underlying pattern in brain activity in healthy individuals versus patients with a brain degenerative disorder. The neural data comes from ECoG (electrocorticography) applied to either humans or primates. Each ECoG array has electrodes that measure voltage variations which neuroscientists claim correlates to neurons transmitting signals to one another. ECoG differs from the less invasive technique of EEG (electroencephalography) in that EEG electrodes are placed above a patients scalp while ECoG involves drilling small holes in the skull to allow electrodes to be closer to the brain. Because of this ECoG boasts an exceptionally high signal-to-noise ratio and less susceptibility to artifacts than EEG [6]. While wearing the ECoG caps, the patients are asked to perform a range of different tasks. The tasks performed by patients are partitioned into different levels of mental stress i.e. how much concentration is presumably required. The specific dataset used in this thesis is derived from cognitive behavior experiments performed on primates at MGH (Massachusetts General Hospital). The content of this thesis can be thought of as a pipelined process. First the data is collected from the ECoG electrodes, then the data is pre-processed via signal processing techniques and finally the data is clustered via unsupervised learning techniques. For both the pre-processing and the clustering steps, different techniques are applied and then compared against one another. The focus of this thesis is to evaluate clustering techniques when applied to neural data. For the pre-processing step, two types of bandpass filters, a Butterworth Filter and a Chebyshev Filter were applied. For the clustering step three techniques were applied to the data, K-means Clustering, Spectral Clustering and Self-Tuning Spectral Clustering. We conclude that for pre-processing the results from both filters are very similar and thus either filter is sufficient. For clustering we conclude that K- means has the lowest amount of overlap between clusters. K-means is also the most time-efficient of the three techniques and is thus the ideal choice for this application.2016-10-27T00:00:00

Clustering by soft-constraint affinity propagation: Applications to gene-expression data

Motivation: Similarity-measure based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing techniques was proposed by Frey and Dueck \cite{Frey07}. In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to, and exemplars have to refer to themselves. Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar per cluster restricts AP to classes of regularly shaped clusters, and leads to suboptimal performance, {\it e.g.}, in analyzing gene expression data. Results: This limitation can be overcome by relaxing the AP hard constraints. A new parameter controls the importance of the constraints compared to the aim of maximizing the overall similarity, and allows to interpolate between the simple case where each data point selects its closest neighbor as an exemplar and the original AP. The resulting soft-constraint affinity propagation (SCAP) becomes more informative, accurate and leads to more stable clustering. Even though a new {\it a priori} free-parameter is introduced, the overall dependence of the algorithm on external tuning is reduced, as robustness is increased and an optimal strategy for parameter selection emerges more naturally. SCAP is tested on biological benchmark data, including in particular microarray data related to various cancer types. We show that the algorithm efficiently unveils the hierarchical cluster structure present in the data sets. Further on, it allows to extract sparse gene expression signatures for each cluster.Comment: 11 pages, supplementary material: http://isiosf.isi.it/~weigt/scap_supplement.pd

Solution Path Clustering with Adaptive Concave Penalty

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of the data shows specific grouping patterns. To address these emerging challenges, we develop a new clustering methodology that introduces the idea of a regularization path into unsupervised learning. A regularization path for a clustering problem is created by varying the degree of sparsity constraint that is imposed on the differences between objects via the minimax concave penalty with adaptive tuning parameters. Instead of providing a single solution represented by a cluster assignment for each object, the method produces a short sequence of solutions that determines not only the cluster assignment but also a corresponding number of clusters for each solution. The optimization of the penalized loss function is carried out through an MM algorithm with block coordinate descent. The advantages of this clustering algorithm compared to other existing methods are as follows: it does not require the input of the number of clusters; it is capable of simultaneously separating irrelevant or noisy observations that show no grouping pattern, which can greatly improve data interpretation; it is a general methodology that can be applied to many clustering problems. We test this method on various simulated datasets and on gene expression data, where it shows better or competitive performance compared against several clustering methods.Comment: 36 page