PSTH-based classification of sensory stimuli using ensembles of single neurons
Introduction
From a computational modeling point of view, the neural code can be studied by simulating the encoding of information in more or less realistic models of neural networks (Diesmann et al., 1999, Kepecs et al., 2002; Moxon et al., 2003a, Moxon et al., 2003b; Passaglia et al., 1997, Poirazi et al., 2003, Rodriguez and Levy, 2001); the ability of such models to reproduce natural behaviors can provide new insights into the underlying system. From an experimental point of view, the neural code can be studied by recording activity of populations of neurons in vivo (Gerstein and Perkel, 1969, Nicolelis et al., 1997a, Moxon et al., 1999, Kralik et al., 2001) in response to known events or stimuli; the performance of a specific algorithm in decoding information from the neural responses allows inferences to be made about the coding strategies actually employed by the recorded neurons (Bialek et al., 1991, de Charms and Merzenich, 1996, de Ruyter van Steveninck et al., 1997, Georgopoulos et al., 1986, Lee et al., 1988, Lewis and Kristan, 1998, McAlpine et al., 2001, Nirenberg and Latham, 2003, Pasupathy and Connor, 2002, Petersen et al., 2001, Young and Yamane, 1992).
The experimental decoding approach has been widely applied to study how neurons in the visual system code for image features (Geisler et al., 1991, Gochin et al., 1994, McClurkin et al., 1991, Optican and Richmond, 1987, Richmond and Optican, 1990, Rolls et al., 1997, Rolls et al., 1998, Victor and Purpura, 1996) and how neurons in the somatosensory system code for stimulus location (Ghazanfar et al., 2000, Nicolelis et al., 1997b, Nicolelis et al., 1998, Panzeri et al., 2001, Petersen et al., 2001, Petersen et al., 2002). The stimulus-related information can be decoded using two main approaches: information theory (McClurkin et al., 1991, Optican and Richmond, 1987, Panzeri et al., 2001, Petersen et al., 2001, Richmond and Optican, 1990) or classification analysis (Ghazanfar et al., 2000, Gochin et al., 1994, Nicolelis et al., 1997b, Nicolelis et al., 1998, Rolls et al., 1997, Rolls et al., 1998). The information theory approach is more rigorous, but computationally very intense and can be applied only on few neurons at a time. Conversely, the classification approach can be easily extended to large numbers of neurons and is more intuitive: given the response of a population of neurons to a set of stimuli, which stimulus generated the response on a single-trial basis?
We are particularly interested in how ensembles of neurons in the somatosensory system encode sensory information. In this paper we focus on the rat trigeminal system because of the discrete layout of the receptive field and because it has been studied in detail with both information theory (Panzeri et al., 2001, Petersen et al., 2002) and classification approaches (Ghazanfar et al., 2000, Nicolelis et al., 1997b, Nicolelis et al., 1998). On one hand, Nicolelis et al. (1998) showed that, somewhat surprisingly, classification performance does not change when using a relatively simple method such as linear discriminant analysis (LDA) (see also Deadwyler et al., 1996, Ghazanfar et al., 2000, Gochin et al., 1994, Nicolelis et al., 1997b, Schoenbaum and Eichenbaum, 1995) compared to more complex methods based on artificial neural networks (ANNs), such as back propagation (see also Hertz et al., 1992, Kjaer et al., 1994, Middlebrooks et al., 1994) or linear vector quantization (LVQ) (Kohonen, 1987, Kohonen, 1997; see also Ghazanfar et al., 2000). Moreover, classification performance does not improve after preprocessing stages that reduce the dimensionality of the data (Nicolelis et al., 1998), such as principal component analysis (PCA) (Jackson, 1991) and independent component analysis (ICA) (Bell and Sejnowski, 1995, Laubach et al., 1999). On the other hand, Panzeri et al. (2001) showed with a rigorous theoretic approach that the average neural responses, i.e. the PSTHs (Gerstein and Kiang, 1960; Fig. 1), describe more than 80% of the information about stimulus location carried by somatosensory cortical neurons. Therefore, we developed a PSTH-based classification method aiming to maximize computational efficiency rather than classification performance, for the long term goal of studying somatosensory coding strategies in large populations of neurons.
In Section 2.1 the PSTH-based method will be presented in general terms and then it will be validated by applying it to typical neural data from the rat whisker cortex in Section 2.2, performing the following analyses. First, in order to test the strengths and the limits of the method, PSTH-based classification performance will be evaluated after standard manipulations of the dataset: changing the size of the response window (‘window selection’), the binsize (‘bin clumping’), the number of whiskers to be discriminated (‘whisker dropping’), the number of training trials (‘trial dropping’), and the number of variables employed for the classification (‘variable dropping’). Second, the PSTH-based classification method will be compared in detail with LDA, which is the method that was shown to provide the best results with the lowest computational complexity in experimental conditions similar to ours (Nicolelis et al., 1998). Finally, the method will be compared to five other methods that either relax some of LDA assumptions (quadratic discriminant analysis, Mahalanobis discriminant analysis) or are potential alternative of the PSTH-based method in term of minimal computational complexity (dot product decoding as in Rolls et al., 1997, Rolls et al., 1998, simplified maximum likelihood classification and Minkowski classification).
Section snippets
Method definition
The general dataset organization is shown in Fig. 2 (Nicolelis et al., 1997b). Single-trial neural responses are grouped in sets of S possible stimuli. Each stimulus in the set is repeated T times in the experiment, while the activity of a population of N single neurons is recorded. For every neuron, a suitable peri-stimulus time window that includes the response is considered. The window is divided into B bins containing spike counts with a desired temporal precision, in order to preserve
Results
The PSTH-based classification method was applied on three populations of 24, 17 and 15 neurons. The neurons that comprise each population were simultaneously recorded from the somatosensory whisker cortex (layer V) of three different rats, with aim of decoding from the neural responses which whisker was contacted on a single-trial basis. The following results are organized into three sections. In the first section the performance of the PSTH-based method will be described as a function of the
Discussion
We developed a PSTH-based method to classify stimulus location using the responses of populations of neurons on a single-trial basis. The method consists of creating a set of templates based on the average neural responses to stimuli (i.e. the PSTHs), and classifying each single-trial by assigning it to the stimulus with the ‘closest’ template in the Euclidean distance sense. The effectiveness of the method was tested under different conditions by manipulating the raw neural data. The main
Acknowledgements
We thank Luiz A. Baccalá for helpful discussions. This work was supported by a grant from the National Institute of Health, NIH 2P50NS24707.
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