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Extension and Comparing the PSTH and ICA in Order to Extract Information from Neural Point Processes

Heidarieh, Mohsen | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 55749 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Jahed, Mehran; Ghazizadeh, Ali
  7. Abstract:
  8. The quantity and quality of information extracted from the brain, in addition to data collection methods, is also related to the statistical tools used. As extracting maximum information in both temporal and spatial dimension require electrophysiological approaches on the physical side, the statistical methods should be optimized to that end, on the theoretical side. The time histogram method is the most basic tool for capturing a time-dependent rate of neuronal spikes. Generally, in the neurophysiological literature, the bin size that critically determines the goodness of the fit of the time histogram to the underlying spike rate has been subjectively selected by individual researchers. Here, a method for objectively selecting the bin size from the spike count statistics alone is introduced, so that the resulting bar or line graph time histogram best represents the unknown underlying spike rate. For this purpose, we first introduce a measurement that specify the goodness of the histogram bandwidth selection. Secondly, some methods, namely "hierarchical", "Semi K-means" and "induction" methods, for accessing the best histogram have been introduced. Then the synthetic and empirical data is used to analyze the performance of the methods and the superiority of the presented method is indicated against other methods.At the next phase of this thesis, networks of neurons are studied to determine the path of information in the brain. The brain can create a sparse representation of the environment and then combine these representations in downstream areas to create rich multisensory responses to support various cognitive and motor functions. Determining the components present in neuronal responses in a given region is key to decipher its functional role and connection with upstream areas. One approach for parsing out various sources of information in a single neuron is by using linear blind source separation (BSS) techniques. However, applying linear techniques to neuronal spiking activity, is likely to be suboptimal due to inherent and unknown nonlinearity of neuronal responses to inputs. This paper proposes a nonlinear Sparse Component Analysis (SCA) method to separate jointly sparse inputs to neurons with post summation nonlinearity, or SCA for Post-Nonlinear neurons (named SCAPL). Specifically, a linear clustering approach followed by Principle Curve Regression (PCR) and a nonlinear curve fitting are used to separate sources. Analysis using simulated data shows that SCAPL accuracy outperforms ones obtained by linear SCA as well as other separating methods including linear independent and principle component analyses (ICA and PCA respectively). In SCAPL, the number of derived sparse components is not limited by the number of neurons unlike most BSS methods. Furthermore, this method allows for a broad range of post summation nonlinearities which could differ among neurons. The sensitivity of our method to noise, joint sparseness, degree and shape of nonlinearity and mixing ill-conditions are further discussed and compared with existing methods. Our results show that the proposed method can successfully separate input components in a population of neurons provided that they are temporally sparse to some degree. Application of SCAPL should facilitate comparison of functional roles across regions by parsing various elements present in a region
  9. Keywords:
  10. Blind Sources Separation (BSS) ; Independent Component Analysis (ICA) ; Poisson Process ; Point Process ; Principal Component Analysis (PCA) ; Inductive Method ; Peri-Stimulus Time Histogram (PSTH) ; Nonlinear Sparse Component Analysis ; Firing Rate ; Hierarchical Optimization

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