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## Subspace Projection Approaches to Classification and Visualization of Neural Network-Level Encoding Patterns

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465 | Regularized discriminant analysis. - Friedman - 1989 |

271 | Real-time prediction of hand trajectory by ensembles of cortical neurons in primates - Wessberg, Stambaugh, et al. - 2000 |

228 |
Neural networks for pattern recognition
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- 1995
(Show Context)
Citation Context ...n equal to the MDA subspace. Artificial Neural Networks (ANN) The Artificial Neural Networks (ANN) employed in this paper are feed-forward Multi-Layer Perceptrons with back-propagation training (MLP, =-=[9,33]-=-). They are capable of performing complex non-linear mapping between the training data and their class membership, and they have been successfully used to analyze neural datasets [34–36]. The type of ... |

116 | Intensity versus identity coding in an olfactory system,” - Stopfer, Jayaraman, et al. - 2003 |

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Citation Context ...ameters at a time. The methods discussed in this paper focus on discrete methods, however, even responses that are modulated by continuous variables can still embedded in a lower dimensional subspace =-=[25,26]-=-. The noise subspace accounts for variability in neural responses in response to stimuli or it may reflect changes in the internal states that are unrelated to changes in experimental conditions. In t... |

86 | 2001): The elements of statistical learning: Data mining, inference, and prediction - HASTIE, TIBSHIRANI, et al. |

80 |
Transient dynamics versus fixed points in odor representations by locust antennal lobe projection neurons.
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Citation Context ...erformances for the training and test data sets. These two eigenvalue/eigenvector techniques are very useful for extracting the essential features down to an encoding subspace of lower dimensionality =-=[5,18,20]-=-, allowing for easier visualization and monitoring of the recorded dynamics. Being linear in nature, they may be the first methods employed in attempting to find low-dimensional classifying subspaces ... |

73 | Large-scale recording of neuronal ensembles. Nat Neurosci 7: 446–451 - Buzsáki - 2004 |

52 |
Rank-Defficient and Discrete Ill-Posed Problems.
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(Show Context)
Citation Context ...ion of equation of form S x=b (which involves a formal inversion of matrix S), which can be achieved by slightly incrementing all diagonal elements in S by a constant factor (Tikhonov regularization, =-=[22]-=-). The optimization problem can now be defined as finding the vector x that minimizes the quantity ||S x2b|| 2 +l 2 ||x|| 2 , where b is a column vector, ||x|| indicates the norm of x, and l is a posi... |

48 | Hirase H, Dragoi G, Buzsáki G. 2003. Organization of cell assemblies in the hippocampus. Nature 424:552 - KD, Csicsvari |

41 |
An information-maximization approach to blind separation and blind deconvolution.
- AJ, TJ
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(Show Context)
Citation Context ...phalography, Functional magnetic resonance imaging) other methods, such as Independent Component Analysis (ICA), may be better suited for separating the continuous signals into independent components =-=[15,16]-=-. MDA is a supervised dimensionality-reduction method that attempts to obtain maximum separation between neural population responses corresponding to different types of known stimuli by identifying an... |

41 | Representations of faces and body parts in macaque temporal cortex: a functional MRI study. - Pinsk - 2005 |

38 |
Neural ensemble coding in inferior temporal cortex.
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(Show Context)
Citation Context ...gnal classification literature is to assume that all neural signals are uncorrelated, that is, to set the non-diagonal elements of the matrix S to zero, thus ensuring that its determinant is non zero =-=[13,14]-=-. These methods may also require further regularization if the sampled neural population contains units with extremely low firing rates, which have mean and standard deviations close to zero; in this ... |

28 |
Hippocampal ensemble activity during spatial delayednonmatch-to-sample performance in rats.
- DEADWYLER
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(Show Context)
Citation Context ...upervised statistical method that can be used to separate neural responses corresponding to different stimuli paradigms into distinct classes [5,30,31], (also known as Canonical Discriminant Analysis =-=[32]-=-, or Quadratic Discriminant Analysis [10–12]). The mean responses during rest and activated states are computed for the training data and used to calculate the between-class scatter matrix SB~ XC i~1 ... |

28 | Serruya MD, Friehs GM, Mukand JA, Saleh M, et al. (2006) Neuronal ensemble control of prosthetic devices by a human with tetraplegia. Nature 442 - LR |

23 | Encoding and decoding of overlapping odor sequences. Neuron - BM, Jayaraman, et al. - 2006 |

23 | Simultaneous encoding of tactile information by three primate cortical areas. - MAL, AA, et al. - 1998 |

22 | JC (2002) Cortical representation of auditory space: information-bearing features of spike patterns - Furukawa, Middlebrooks |

22 |
Tootell RB, Livingstone MS. 2006. A cortical region consisting entirely of face-selective cells
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(Show Context)
Citation Context ...e/decrease of frequency responses of neuron i during the j th face presentation and g j is the noise term. As it appears that neural responses might be also described by a hierarchical representation =-=[38,40]-=-, we choose an example supporting this view, with neural subpopulations responding to either single perceptions or multiple selective combinations of face perceptions (See illustration in Figure 1C). ... |

18 |
Mitra PP (2004) Multiple neural spike train data analysis: State-of-the-art and future challenges. Nat Neurosci 7: 456–461
- EN, RE
(Show Context)
Citation Context ...e cross-correlations and joint peri-event time histograms) statistics of time series of discrete spike trains (point process) are no longer adequate to deal with the complexity of the large data sets =-=[7,8]-=-. In this paper we examine methods for categorical classification of discrete stimuli or episodic events based on the spike series responses they induce in a population of neurons. In addition, we foc... |

16 |
Wavelet-based processing of neuronal spike trains prior to discriminant analysis
- Laubach
- 2004
(Show Context)
Citation Context ...inant Analysis Multiple Discriminant Analysis (MDA) is a supervised statistical method that can be used to separate neural responses corresponding to different stimuli paradigms into distinct classes =-=[5,30,31]-=-, (also known as Canonical Discriminant Analysis [32], or Quadratic Discriminant Analysis [10–12]). The mean responses during rest and activated states are computed for the training data and used to c... |

15 | Statistical encoding model for a primary motor cortical brainmachine interface
- Shoham, Paninski, et al.
- 2005
(Show Context)
Citation Context ...ameters at a time. The methods discussed in this paper focus on discrete methods, however, even responses that are modulated by continuous variables can still embedded in a lower dimensional subspace =-=[25,26]-=-. The noise subspace accounts for variability in neural responses in response to stimuli or it may reflect changes in the internal states that are unrelated to changes in experimental conditions. In t... |

11 |
Using multi-neuron population recordings for neural prosthetics.
- JK
- 2004
(Show Context)
Citation Context ...e cross-correlations and joint peri-event time histograms) statistics of time series of discrete spike trains (point process) are no longer adequate to deal with the complexity of the large data sets =-=[7,8]-=-. In this paper we examine methods for categorical classification of discrete stimuli or episodic events based on the spike series responses they induce in a population of neurons. In addition, we foc... |

10 | CR, Nicolelis MA (2000) Encoding of tactile stimulus location by somatosensory thalamocortical ensembles - AA, Stambaugh |

9 |
Zuo W, et al. (2005) Identification of networklevel coding units for real-time representation of episodic experiences in the hippocampus. Proc Natl Acad Sci U S A 102: 6125–6130
- Lin, Osan, et al.
(Show Context)
Citation Context ...ible. Another way of addressing this problem is through preprocessing, by eliminating such low-firing neurons or other units that have weak changes in firing rates between different stimuli paradigms =-=[5]-=-. The main consequence of the regularization methods mentioned in the previous paragraph is to increase the relative size of diagonal elements as compared to off-diagonal elements. We Figure 2. Regula... |

9 |
Tsien JZ (2006) Molecular and systems mechanisms of memory consolidation and storage. Prog Neurobiol 79
- Wang, Hu
(Show Context)
Citation Context ...periment. The application of sliding window technique to MDA has led to the direct visualization of encoding and reactivations of ensemble traces during formation of episodic memory [5,20], (see also =-=[27,28]-=-). In conclusion, we have systematically compared the performance of several multivariate statistical methods on large neural data sets and we have found the following ranking MDA.PCA.ANN.MGD. Our emp... |

8 |
Eichenbaum H
- Schoenbaum
- 1995
(Show Context)
Citation Context ...gnal classification literature is to assume that all neural signals are uncorrelated, that is, to set the non-diagonal elements of the matrix S to zero, thus ensuring that its determinant is non zero =-=[13,14]-=-. These methods may also require further regularization if the sampled neural population contains units with extremely low firing rates, which have mean and standard deviations close to zero; in this ... |

4 |
M (1998b) Methods for simultaneous multisite neural ensemble recordings in behaving primates. In: Methods for neuronal ensemble recording (Nicolelis MA, ed). Boca
- MA, CR, et al.
(Show Context)
Citation Context ...a few seconds. Previous research in primary sensory and motor regions suggests that multivariate methods perform better when the bin sizes used to create the input data sets have a width above 100 ms =-=[21]-=-. For our data sets we choose to partition a one-second time interval in two bins, to include information about the initial activation and the subsequent sustained activity, while choosing time bins l... |

4 |
O’Leary DP
- GH
- 1989
(Show Context)
Citation Context ...ively defined regularization parameter. An appropriate choice for the l values should be a good compromise between too little (l =0, overfitting) or too much filtering (l large), and earlier research =-=[23,24]-=- suggest that appropriate values lie at the corner of the so-called L-curve plot that displays the log(||S x2b||) vs. log(||x||). While this method provides automatic selection for the regularization ... |

3 |
Sgallari F (2000) Tikhonov regularization and the l-curve for large discrete ill-posed problems
- Calvetti, Morigi, et al.
(Show Context)
Citation Context ...ively defined regularization parameter. An appropriate choice for the l values should be a good compromise between too little (l =0, overfitting) or too much filtering (l large), and earlier research =-=[23,24]-=- suggest that appropriate values lie at the corner of the so-called L-curve plot that displays the log(||S x2b||) vs. log(||x||). While this method provides automatic selection for the regularization ... |

3 |
Neonatal whisker removal reduces the discrimination of tactile stimuli by thalamic ensembles in adult rats
- MA, RC, et al.
- 1997
(Show Context)
Citation Context ...inant Analysis Multiple Discriminant Analysis (MDA) is a supervised statistical method that can be used to separate neural responses corresponding to different stimuli paradigms into distinct classes =-=[5,30,31]-=-, (also known as Canonical Discriminant Analysis [32], or Quadratic Discriminant Analysis [10–12]). The mean responses during rest and activated states are computed for the training data and used to c... |

2 |
Tibshirani R (2007) Regularized discriminant analysis and its application in microarrays
- Guo, Hastie
(Show Context)
Citation Context ...1, Si is the covariance matrix for the i th class, and I is the identity matrix. As a result of regularization the determinant becomes non-zero and matrices S i can be now inverted. Previous research =-=[12]-=- used cross-validation results to search for the optimal regularization parameter. Here, we suggest an automatic way of selecting these parameters in the next paragraph, as this allows us to use the c... |

1 | CS, Nicolelis MA (2005) Stable Ensemble Performance with Single-Neuron Variability during Reaching Movements in Primates - JM, MA, et al. |

1 | RA (2006) Electrophysiological Mapping of Cat Primary Auditory Cortex with Multielectrode Arrays. Ann Biomed Eng 34 - SJ, SC, et al. |

1 | Zaia K, Zhang S, et al. (2006a) Large-scale neural ensemble recording in the brains of freely behaving mice - Lin, Chen |

1 |
Sejnowski T (2001) Independent component analysis at the neural cocktail party. Trends Neurosc 24: 54–63
- GD, Yamada
(Show Context)
Citation Context ...phalography, Functional magnetic resonance imaging) other methods, such as Independent Component Analysis (ICA), may be better suited for separating the continuous signals into independent components =-=[15,16]-=-. MDA is a supervised dimensionality-reduction method that attempts to obtain maximum separation between neural population responses corresponding to different types of known stimuli by identifying an... |

1 |
Tsien JZ (2006b) Organizing principles of real-time memory encoding: neural clique assemblies and universal neural codes. Trends Neurosci
- Lin, Osan
(Show Context)
Citation Context ...erformances for the training and test data sets. These two eigenvalue/eigenvector techniques are very useful for extracting the essential features down to an encoding subspace of lower dimensionality =-=[5,18,20]-=-, allowing for easier visualization and monitoring of the recorded dynamics. Being linear in nature, they may be the first methods employed in attempting to find low-dimensional classifying subspaces ... |

1 | Processing the facial image: a brief history. Am Psychol 60: 755–63 - CG - 1992 |

1 |
Processing the facial image: a brief history
- CG
- 2005
(Show Context)
Citation Context ...e/decrease of frequency responses of neuron i during the j th face presentation and g j is the noise term. As it appears that neural responses might be also described by a hierarchical representation =-=[38,40]-=-, we choose an example supporting this view, with neural subpopulations responding to either single perceptions or multiple selective combinations of face perceptions (See illustration in Figure 1C). ... |

1 | Adaptive behavior of cortical neurons during a perturbed arm-reaching movement in a nonhuman primate. Prog Brain Res 143 - DJ, He - 2004 |