Spiking neural networks (SNNs) with adaptive synapses reflect core properties of nearly all biological networks. An important mechanism of Hebbian synaptic modification in biological networks is known as spike-timing-dependent plasticity (STDP) [1, 2]
. STDP-type mechanisms take into account the relative spike times of pre- and postsynaptic neural spikes to adjust the strength of a synapse connecting two neurons. The question of what STDP accomplishes in a learning framework is, and has been, under intense investigation. Spiking neurons and STDP learning rules have been applied in diverse fields of pattern recognition and classification[3, 4, 5, 6, 7, 8] such as learning and information processing of visual features [9, 10, 11] and speech recognition [12, 13].
Our work studies the performance of a novel STDP-trained, nonrecurrent SNN for isolated spoken digit recognition. The spike trains produced by the output neurons in this network have discriminative properties. That is, the spike signature of an output neuron contains substantial information about the digit presented to the network. The net input to these neurons, which drives their output spikes, can be used to train a support-vector machine (SVM) to recognize the presented digit. The information encoded in a spike train is an example of temporal coding.
The learning is applied to the output neurons and uses a mixture of Hebbian and anti-Hebbian STDP in a supervised fashion. Specifically, if an output unit is being trained to recognize the spoken digit “one,” then it undergoes Hebbian STDP when an exemplar of “one” is presented and anti-Hebbian STDP otherwise.
Our proposed architecture is a small feedforward network of spiking neurons that is trained by using the combination of supervised Hebbian and anti-Hebbian STDP just described. The learning has two effects. First, the net inputs to the output neurons can be used to train an SVM for spoken digit recognition. Second, the output spike trains have discriminative properties and, in principle, could be used to perform the classification task.
The small network is efficient and can be trained (or used) quickly, while showing promising accuracy. Also, the trained synaptic weights extract input signatures invariant to different speakers (male and female) and signal variants.
1.1 Related work
We discuss two approaches to using spiking neural networks in spoken digit classification. The first approach uses feedforward-architectures because our network is a single-layer feedforward network. The second approach uses a recurrent architecture in the form of a liquid state machine (LSM).
1.1.1 Comparable work
Much research has studied neurocomputational approaches to ASR mimicking the biological inspiration of the human auditory system [14, 15, 16]. The auditory system has components for encoding the raw signal (inner ear) and generating appropriate spike trains (cochlea).
Schafer and Jin 
developed a template-based, single-layer network architecture for spoken digit recognition. Its emphasis is on recognizing noise-corrupted, spoken digits. The network consists of 32 input units fully connected to up to 1,100 output units. The input units are driven by a bank of 32 cochlear gammatone filters that process the speech signal. Each output unit is separately trained by a support-vector machine (SVM) to respond to a particular preprocessed acoustic feature and, in response to speech input, generates a spike train. The collection of spike trains from each of the output neurons compose a spike raster, which is taken as the network output. The output spike raster is compared to prototype rasters using a longest-common-substring (LCS) algorithm to classify the input signal. To support different pronunciations and signal variations, they used up to 100 prototype-templates per digit. They reported 82% to 99% accuracy rates for the networks using a range of 1 to 100 templates per digit. Our work differs from theirs in two important ways. First, our work uses a biologically plausible STDP algorithm to train the output units. Second, we use ten output units, in contrast to 1,100, and each of our units detects one digit. Their output units detect speech formant features and our output units detect digits. We use an output signature of a single neuron, instead of a spike raster of features, to recognize a digit.
Wade et al  introduced a learning method that merges the STDP rule with the BCM  learning rule (so that the acquired weights are more stable). Their spiking network was two-layer with 5040 neurons in the hidden layer and ten neurons in the output layer, representing each of the ten digit classes. In the output layer, the neuron with the highest firing rate determines the classification decision. This contrasts with our network where the output neuron’s spike signature is more relevant to the classification decision. They also used a highly speculative global weight mapping rule (hypothesized to be mediated by astrocytes) to control the relative occurrence of similar data patterns across classes. They evaluated their model using different benchmark problems including spoken digit recognition. The SNN proposed by Wade et al. consists of frequency-selective filters followed by a layer which undergoes local learning. This network uses 50,400 adaptive synapses, so it is a much larger network than ours (which uses 2,000 synapses).
Dibazar et al. proposed a feature extraction method using a continuous dynamic synaptic neural network to implement a biologically plausible network for spoken digit recognition by a classifier[19, 14]. They achieved 99% and 40% accuracy rates for clean and noisy (10 dB) signals respectively, but at the expense of high computational complexity. Later, they developed a biologically plausible discrete dynamic NN to extract features from the speech signal with 85% and 45% accuracy rates for clean and noisy (10 dB) spoken digits. In this architecture, much of the information is encoded in the real-time dynamics of the synapses. Our network uses static, adjustable synapses so the network operation is fundamentally different.
Dao et al  introduced a sparsity-based representation for spoken digit recognition. Although they did not use SNNs, the goal for fast processing and effective signal discrimination for pattern recognition was accomplished.
1.1.2 Reservoir-based approaches
for a review of reservoir-based approaches in general. As a whole, this work has been quite successful in achieving near perfect digit recognition performance with robustness to noise. Reservoirs were proposed as a solution to the slow convergence of recurrent neural networks, which were of interest because of their ability to store temporal information. Reservoir computing avoids the convergence issue by using a suitably structured RNN as a reservoir (temporal memory) which is not trained. A good reservoir operate on the edge chaos and implements a fading memory. The reservoir can consist of either spiking or non-spiking  neurons. Training is reserved for a linear readout layer that trains rapidly. The linear readout performs well because the RNN maps the inputs to a higher dimensional space in which the categories are more likely to be linearly separable.
Although the reservoir may or may not be built from spiking neurons, to our knowledge, in the context of speech recognition, there is only one study that use a trainable readout layer with spiking neurons . In most studies, the state of a spiking reservoir is low-pass filtered [21, 22] before being sent to the readout layer. This allows the readout layer to be rapidly trained using any traditional non-spiking method for a single-layer architecture . Zhang et al  is the only study that presented an LSM in which the readout layer was trained using a bio-inspired, spike-based learning rule.
Although the reservoir approach described above yields excellent performance on spoken digit recognition, the question of training a spiking network in the context of speech recognition is not addressed in this research. Also, the operation of reservoir is computationally more expensive than a single-layer, feed-forward SNN. The present paper explores the training of a single layer SNN for extracting the spike train signatures from the spoken digits. Similar to an LSM, our network does train a classifier by using the net inputs to the readout neurons.
2 Feature Extraction
Feature extraction converts a raw signal into a more usable form. The speech signal is divided into small overlapping time sections called speech frames. The Hamming window, which is commonly used in discrete time signal processing, is used in signal framing due to its frequency features . Our SNN needs a fixed number of frames, , for each spoken digit. As the length, , of a spoken digit can vary from 500 to 1000 ms, we divided it into frames with 50% overlap to support a frame length of 10-50 ms. The 50% overlap () captures the temporal characteristics of the changing spectrum of the speech signal. The window size (frame length) in milliseconds is calculated based on , , and , as shown below.
Because window size increases with signal duration, spoken words pronounced slowly have longer frames in comparison to words pronounced quickly.
After framing, a small feature vector for each frame is extracted. There are several methods for speech feature extraction such as MFCC and Mel-scaled discrete wavelet coefficient (MFDWC) . We instead use a minimal feature vector extracted from the frame’s frequency spectrum, as explained below.
2.1 Frequency spectrum
As a speech signal unfolds in time, the power of its frequency spectrum varies. This can be visualized in a spectrogram as shown in Fig. 1. Spectrograms can be used to identify spoken words phonetically, and to analyze the audio files in specific frames. Spectrum calculation of a frame is shown in Eq. (2). The spectrum values are calculated for all the frames temporally to represent the speech signal spectrogram. Fig. 1 shows the spectrogram for the spoken digit .
2.2 Frequency band
Low frequencies in the spectrogram have more energy and information relevant to classification than the high frequencies (cf. Fig. 1). Thus, an effective feature vector provides more resolution in low frequencies. This is obtained by using incrementally spaced frequency bands. We create the frequency bands from the Fibonacci sequence. This sequence provides good frequency band sizes for a small number of features (other approaches to doing this are also viable).
A separate feature vector is calculated for each frame. A frame encompassing an Hz frequency range can be divided into frequency bands. In this paper, Hz and . The number of filter banks () is small enough to create a minimal SNN. Although more feature values characterize the speech frame with higher resolution, the large input vector increases the network’s computations. Therefore, five filter banks are sufficient for this purpose. Additionally, for the isolated spoken digit recognition problem, three filter banks extracting the acoustic features in the range 0 to 1500 Hz are able to represent only eight vowels and one nasal phoneme pronounced in the spoken digits (‘aa’ as one, ‘u’ as two, ‘ee’ as three and zero, ‘o’ as four and zero, ‘ai’ as five and nine, ‘i’ as six, ‘e’ as seven, ‘ei’ as eight, and n). If the first frequency band length is , then the filter bank containing bands will have lengths of . Specifically, each frame represented in the Hz frequency range is divided into bands with lengths of (333.3, 333.3, 666.7, 1000, and 1666.7) as shown in Fig. 2. is chosen so that the equality below is satisfied.
The value of each element in a feature vector is the average energy over the range given in Fig. 2 for a given frame. For example, the first feature value codes the average energy in the range Hz.
3 Input Spike Generation
We use the Izhikevich model regular spiking (RS) neuron  to convert a feature component to a spike train, as seen in Eqs. (4) through (6). Extracted features control the value of the injected input current, , to an afferent unit. The drives the system. For the units, the only input is , so in the equations below. A larger total current causes more frequent spikes as seen in Fig. 3. Also, it can be seen that the neurons exhibit spike-rate adaptation to a constant input (which is a common characteristic of biological neurons).
and the reset equation
The spike time is the time step at which the membrane potential, , becomes greater than . specifies a recovery factor inhibiting the spike and keeps the membrane potential near the resting value, . The neuron capacity (), threshold (), , and symbols are constants, specified in Table 1, whose values control the dynamic characteristics of the system and cause the neuron to have regular spiking behavior.
Each feature vector component drives one RS neuron by controlling the value of ( unit, as explained in the next section), causing it to generate a spike train over a fixed duration milliseconds.
4 Network Architecture
Our network is trained using STDP with labeled data. After training, the network can generate spike train signatures for the ten digit categories. The test signatures can be compared with spike trains from target data to perform classification. The network architecture appears in Fig. 4. It consists of:
For training, the network input consists of feature vector input from frames. The frames cover the duration of the speech input stream. Each feature vector has components as described in Sec. 2. For training, the sequential input is buffered and then presented to the network simultaneously (For testing, the procedure is slightly different). At first glance, it might seem like this might cause the sequential dependencies in the input to be lost. However, this is not the case. The sequence information is simply converted from a temporal to a geometric format. Although the input is pooled for training, the raw sequential information is preserved when generating spike signatures after training (explained in Sec. 5.3).
An output layer of ten units is used. Each unit corresponds to one of the ten spoken digit categories (class labels). These are also implemented as RS neurons with the same parameter configuation as the units (Table 1). Their input consists entirely of synaptic input from the 200 units, namely . The units are fully connected to the units. The units are trained according to the procedure described in Sec. 5.
Finally, there is a teacher that monitors the units in order to determine the form of the STDP used in training. If the target unit spikes at a given time step, it undergoes case 1 of Hebbian STDP and the rest of the (nontarget) units undergo case 1 of anti-Hebbian STDP. If the desired unit does not spike, it undergoes case 2 of Hebbian STDP and the rest of the units undergo case 2 of anti-Hebbian STDP. The teaching signal is only used for the training phase.
There are two types of learning in the model. The most important type is the STDP that is used to train the synapses projecting to the output units. The other type of learning occurs after the synapses are trained. The net input to the trained output units is used to train an SVM for classification (explained in Sec. 6.5).
5.1 Neuron Model
Fig. 5 (left) shows the simulation circuit of a model neuron. The dashed box represents the spike generation step described in Eqs. (4 – 6). The branches marked to represent synaptic conductances for three synapses. If the neuron is a unit, then there is no synaptic input, only injected current . In this case, . For a unit, there is synaptic input , but no injected current. In this case, . Each unit has incoming synapses, corresponding to the 200 afferent units.
Learning occurs by modifying the synaptic conductances. denotes the synaptic conductance change over time for synapse caused by receiving a single input spike to that synapse. The –function (Eq. 7) models the conductance time-course of the synapse. Fig. 5 (right) shows the –function graph for one synapse receiving one spike at time .
controls the conductance amplitude. This is what is adjusted during learning. Synaptic weight adjustments change the value of according to Eq. (11). is the time at which the synapse reaches its maximum conductance. represents the elapsed time since the most recently received spike.
When multiple spikes are received in succession before a conductance drops to zero, the successive conductance effects are added linearly according to Eq. (8). Specifically, the total conductance of input synapses with () spikes is calculated by summing linearly over the synapses and input spikes:
where is the spike time of spike for synapse . denotes the number of spikes received by synapse . The total synaptic current is given by:
In our simulations, .
5.2 Spike Timing Dependent Plasticity (STDP)
Weight adjustment at a synapse is governed by the relative spike times of its pre- and postsynaptic neurons (Eq. 10) in conjunction with the teacher feedback. The teacher feedback dictates the form of the STDP, whether it be Hebbian or anti-Hebbian. In the case of normal Hebbian STDP, if the postsynaptic spike is generated immediately after receiving the presynaptic spike, the presynaptic spike has a causal role in the output neuron firing. The synaptic weight is thus increased (LTP). Conversely, if a postsynaptic spike occurs before the presynaptic spike, the strength is reduced (LTD), as seen in the equation below.
In the above, the first case (Case 1) covers LTP and the second case (Case 2) covers LTD. Both cases are decaying exponentials that decay with the distance between and pre- and postsynaptic spikes. and scale the amplitude of the exponential, and and are the respective time constants.
Eq. (10) describes Hebbian STDP. To obtain anti-Hebbian STDP, we swap the cases. The teacher determines which units undergo Hebbian versus anti-Hebbian STDP. During training, whenever a unit emits a spike, it undergoes some form of STDP. If the unit represents the target category, then it undergoes Hebbian STDP. Otherwise, it undergoes anti-Hebbian STDP.
The synaptic weight change contributes to a change in the conductance amplitude, , in the -function model. We link the weight adjustment to the adjustment of , used in Eq. 7, by using the equation below.
We now summarize the simulation’s operation during training. The simulation is advanced using ms time steps using forward Euler (which is adequate for this problem). The and units are updated in a manner consistent with a feedforward sweep. Whenever a unit fires, the teacher determines which variant of STDP to apply for that unit. We also renormalize the weights, using , after each training sample.
5.3 Obtaining spike signatures
Spike signatures are obtained after training. To obtain a spike signature from an input sample, each input frame is processed individually and sequentially, rather than simultaneously (as was done with training). A frame, which contains 5 feature values, is converted to a spike train (with ms and ms) by passing through the corresponding inputs to the trained network. Each of the forty frames is passed through the network sequentially such that a spike signature of an idealized duration equal to 200 ms is obtained (405 ms).
6 Experimental Methods and Results
6.1 Data Preparation
Our experiments were conducted on the Aurora dataset of isolated spoken digits recorded from different male and female speakers . The dataset was used for three purposes: training the network (500 samples), testing the trained network without noise (500 samples), and testing the trained network with noise (500 noisy samples, SNR=10 dB).
For training, 500 spoken digit samples, with 50 representatives for each digit (0 – 9), were randomly sampled from the dataset. Each sample was divided into 40 frames with 50% overlap Hamming windows, according to Eq. (1
). The feature vector for a frame was obtained by applying the Fourier transform to the wave data and calculating the average energy of the five Fibonacci-scaled bands. This producedfeature vectors of components. These were concatenated into a global feature vector of components. The feature vector values form the input to the units shown in Fig. 4.
Before training the weights were initialized to uniform random values between 0 and 1 and then normalized using the norm. For each training sample, the network operated as follows. The global feature vector for that sample was presented to the units for a duration of milliseconds. The units generated spikes from their respective input as shown in Fig. 3. Each of the ten output neurons received 200 spike trains of duration 100 ms via 200 trainable synapses. The 2,000 incoming synapses to the unit layer were trained such that 200 synapses representing the presented digit category underwent Hebbian STDP and the remaining synapses underwent anti-Hebbian STDP.
The synaptic weights were renormalized after the presentation of each training example. Because convergence was rapid, training was stopped after 100 epochs, each of which consisted of 500 training samples. Fig.6 shows the trained synaptic weights arranged so that they can be compared with a spectrogram like that shown in Fig. 1. Each point in this figure shows the synapse passing a spike train with respect to frame (in the range 1 to 40) and feature value (in the range 1 to 5).
6.3 Testing method
In testing mode the network generates spike signatures. Both prototype and test signatures are generated. Test spike signatures are produced by an output unit by submitting a spoken digit sample to the network after it has been trained. Prototype spike signatures represent the response of an output to an ‘average’ exemplar for the digit class.
6.3.1 Prototype spike signatures
We first explain how prototype spike signatures are generated. These signatures are generated for each of the ten digit categories after training. The trained network is used to generate these signatures. Before generating a prototype spike signature for a given category, we create a representative input feature set for that category. This involves reusing the training data. Specifically, we average over the extracted feature coefficients for each digit class in the training set (50 samples per class) to obtain representative feature input for that class. That yields values for each of ten new representative samples. These ten new items are given to the trained network to generate a prototype spike signature for each category (according to section 5.3). As explained before, each of the forty frames is passed through the network sequentially such that a spike signature of an idealized duration equal to 200 ms is obtained (405 ms). The prototype spike trains appear in Figs. 7 (left) and 8 (left) before and after training respectively.
6.4 Spike signature results
A set of spoken digits 0 to 9, not used in training, was randomly selected to obtain test spike signatures. Testing spike signatures were generated analogously to prototype spike signatures, however, using a single test sample as input for eqch test signature. The resulting test spike trains after training appear in Fig. 8 (right). Each test signature corresponds to a single randomly selected spoken digit. Fig. 7
shows spike train signatures before network training. The spikes are roughly uniformly distributed and dense. Comparison with Fig.8 after training shows that meaningful spike signatures emerge. Comparison between spike signatures in Fig. 8 (left and right) shows that signatures for randomly selected test digits resemble the corresponding prototype signatures. Emitted spikes for the same digits show similar temporal patterns visually. For example, the test signature for a digit six in Fig. 8 (left) is similar to the prototype for category six (right). Specifically, its temporal patterns are similar where they have uniformly distributed spikes between 40 to 80 ms. However, the temporal patterns of the other digits (0-5, 7-9) have a large distance from the digit six target signature. To quantify this, we use the Victor–-Purpura distance metric [32, 33] that quantifies dissimilarity of spike trains. Table 2 shows the distances between target and prototype signatures calculated by the spike interval metric111www-users.med.cornell.edu/~jdvicto/pubalgor.html . The spoken digits 3, 4, and 0 have not been distinguished as accurately as the other digits.
|Prototype||Randomly selected test|
6.5 Classification performance results
A natural approach to classifying spoken digits would be to match its test signature against the set of class prototypes and choose the class with the closest match. Unfortunately, the performance of this approach was not that good. That is, the prototypes obtained from the class average of the input features was not sufficiently precise to support good classification. Instead, a different classification method was implemented that used the net input to the output neurons.
For classification, the net input (obtained from a single exemplar) to an output unit was used to train an SVM. The net input to an output unit was subdivided into forty, 5-millisecond duration frames corresponding to the 200 millisecond input signal. The net input was assumed to be a good indicator of the number of neural spikes generated by that output unit (possibly with a small time delay). In summary, feature vectors used for training the classifier preserved temporal information at the resolution of 40 bins and 5 ms per bin. The net input corresponds to in Fig. 5 in which five input synapses are used (the number of features in a frame).
The performance of the classifier is shown in Table 3. Overall accuracy is 91 percent for the clean test stimuli. Accuracy drops to 70 percent when noisy stimuli are used. To provide more information, specifically, on what types of errors were made, Tables 4 and 5 show confusion matrices for the clean and noisy conditions, respectively.
|Measure||No Noise||10 dB Noise|
|Average Hit Ratio (%)||90.9||70.9|
|Average Misclassification Rate (%)||9.3||29.9|
|Miss rate (%)||10.0||7.4||10.0||7.8||2.0||14.3||13.3||8.8||10.9||8.2||454|
|Miss rate (%)||29.6||31.4||37.0||22.0||10.0||47.9||36.4||27.1||37.3||20.0||351|
6.6 Comparison to other approaches
Our approach with 91% accuracy compares favorably with other recent investigations regarding spike-based neural networks for spoken digit recognition in terms of the combined factors of network complexity and accuracy rate. Table 6 presents a rough comparison of accuracy achieved in other recent studies. The Aurora data set is roughly comparable to the TI46 data set . Aurora is based on a version of the TIDigits data set, but downsampled at 8 kHz using an ‘ideal’ low-pass filter. The clean spoken digits are then distorted artificially.
|Model||Accuracy (%)||# Adaptive weights||Dataset||# Speakers|
|Schaffer & Jin ||82-99||Aurora||100|
|Dao et al ||95||Not SNN||Aurora||–|
|Wade et al ||95.25||TI46||16|
|Verstraeten et al ||97.5, 99.5 (Best)||to||TI46||5|
|Zhang et al ||92.3, 99||TI46||16, 5|
|Dibazar et al ||85.5||TIDigits||–|
7 Discussion and conclusion
Our model represents a novel method for creating spike train signatures from spoken digits. It uses the Izhikevich RS neuron model combined with STDP learning. The learning was implemented by Hebbian and anti-Hebbian STDP controlled by a teaching signal. The trained network produced target spike signatures for the ten spoken digits. Prototype signatures obtained from a set of average input feature values produced similar signatures for the same categories and different signatures for the non-similar categories. The proposed SNN provided a fast spike signature extraction system for both male and female speech signals. A signature-based classifier obtained 91% and 70% overall accuracy rates in categorizing the clean and noisy spoken digits, respectively.
Small, spike-based networks, when appropriately adapted, enable power efficient implementations on neuromorphic hardware. The proposed single-layer SNN uses a small number of spiking neurons and adaptive synapses to implement a fast and efficient model to extract spike signatures for spoken digits. The filter banks extract only five feature values for each frame to create a minimal network while performing reasonably. The Hebbian and anti-Hebbian STDP rules adjust the synaptic weights such that the spatio-temporal features of the speech signal are preserved. The spike signatures extracted for the digits represent different spiking patterns for different digits. The visual comparisons and the distance measures between the prototype and the test spike signatures showed the network has power to discriminate the spoken digits. Additionally, the classification results (91% accuracy) were consistent with the characteristics of the spike signatures. Furthermore, the minimal SNN recognized the noisy spoken digits (10 dB) with 70% accuracy.
Biological networks at least in part use temporal spike codes, as exemplified by the spike signatures we have generated in the present study. The outputs of our network can be used as inputs for further processing such as to identify common digit sequences (e.g., “911”) or more general modules for word-phrase processing.
Therefore, the proposed network is a useful architecture of spiking neurons to extract feature sets to be used for classification problems. In the future investigations, this network can be assigned as the first layer (component) of a spiking deep neural network when its feature maps are used as an input set of spike trains for the next layers of spiking neurons. A limitation of the proposed method comes from the trade-off with its complexity and performance. The small feature vector used in this model does not extract fine details of the signal and would not be a sufficiently sensitive detector for larger vocabularies.
-  N. Caporale and Y. Dan. Spike timing-dependent plasticity: a Hebbian learning rule. Annual Reviews of Neuroscience, 31:25–46, 2008.
-  Henry Markram, Wulfram Gerstner, and Per Jesper Sjöström. A history of spike-timing-dependent plasticity. Spike-timing dependent plasticity, page 11, 2011.
-  N. Kasabov, K. Dhoble, N. Nuntalid, and G. Indiveri. Dynamic evolving spiking neural networks for on-line spatio and spectro-temporal pattern recognition. Neural Networks, 41:188–201, 2013.
A. Kasinski and F. Ponulak.
Comparison of supervised learning methods for spike time coding in spiking neural networks.International Journal of Applied Mathematics and Computer Science, 16:101–113, 2006.
-  J. Storck, F. Jakel, and G. Deco. Temporal clustering with spiking neurons and dynamic synapses: towards technological applications. Neural Networks, 14(3):275–285, 2001.
-  S. G. Wysoski, L. Benuskova, and N. Kasabov. Evolving spiking neural networks for audiovisual information processing. Neural Networks, 23(7):819–835, 2010.
-  C. Panchev and S. Wermter. Spike-timing-dependent synaptic plasticity: from single spikes to spike trains. Neurocomputing, 58:265–371, 2004.
-  J. Wang, A. Belatreche, L. Maquire, and T. M. McGinnity. An online supervised learning method for spiking neural networks with adaptive structure. Neurocomputing, 144:526–536, 2014.
-  T. Masquelier and S. J. Thorpe. Unsupervised learning of visual features through spike timing dependent plasticity. PLoS Computational Biology, 3(2):247–257, 2007.
-  Amirhossein Tavanaei, Timothee Masquelier, and Anthony S Maida. Acquisition of visual features through probabilistic spike-timing-dependent plasticity. In International Joint Conference on Neural Networks (IJCNN), pages 307–314, 2016.
-  S. G. Wysoski, L. Benuskova, and N. Kasabov. Fast and adaptive network of spiking neurons for multi-view visual pattern recognition. Neurocomputing, 71(13):2563–2575, 2008.
-  J. J. Wade, L. J. McDaid, J. Santos, and H. M. Sayers. SWAT: a spiking neural network training algorithm for classification problems. IEEE Transactions on Neural Networks, 21(11):1817–1830, 2010.
Amirhossein Tavanaei and Anthony S Maida.
Training a hidden markov model with a bayesian spiking neural network.Journal of Signal Processing Systems, pages 1–10, 2016.
-  A. Dibazar, D. Song, W. Yamada, and T. W. Berger. Speech recognition based on fundamental principles of the brain. In IEEE 2004 International Joint Conference on Neural Networks, pages 3071–3075, 2004.
-  C. Näger, J. Storck, and G. Deco. Speech recognition with spiking neurons and dynamic synapses: a model motivated by the human auditory pathway. Neurocomputing, 44:937–942, 2002.
-  H. H. Narmavar, J. S. Liaw, and T. W. Berger. A new dynamic synapse neural network for speech recognition. In IEEE 2001 International Joint Conference on Neural Networks, pages 2985–2990, 2001.
-  Phillip B Schafer and Dezhe Z Jin. Noise-robust speech recognition through auditory feature detection and spike sequence decoding. Neural computation, 26(3):523–556, 2014.
-  Elie L Bienenstock, Leon N Cooper, and Paul W Munro. Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. The Journal of Neuroscience, 2(1):32–48, 1982.
-  A. A. Dibazar, H. H. Namarvar, and T. W. Berger. A new approach for isolated word recognition using dynamic synapse neural networks. In IEEE 2003 International Joint Conference on Neural Networks, pages 3146–3150, 2003.
-  Minh Dao, Yuanming Suo, Sang Peter Chin, and Trac D Tran. Structured sparse representation with low-rank interference. In 2014 48th Asilomar Conference on Signals, Systems and Computers, pages 106–110. IEEE, 2014.
-  D. Verstraeten, B. Schrauwen, D. Stroobandt, and J. V. Campenhout. Isolated word recognition with the Liquid State Machine: a case study. Information Processing Letters, 95(6):521–528, 2005.
-  D. Verstraeten, B. Schrauwen, and D. Stroobandt. Reservoir-based techniques for speech recognition. In Proc 2006 Intl Joint Conf on Neural Networks, pages 1050–1052, Vancouver, July 2006.
-  B. Schrauwen, J. Defour, D. Verstraeten, and J. V. Campenhout. The introduction of time-scales in reservoir computing, applied to isolated digits. In Artificial Neural Networks – ICANN 2007, pages 471–479. Springer, 2007.
-  M. D. Skowronski and J. G. Harris. Automatic speech recognition using a predictive echo state network classifier. Neural Networks, 20(3):414–423, 2007.
-  A. Ghani, M. McGinnity, L. P. Maquire, and J. Harkin. Neuro-inspired speech recognition with recurrent spiking neurons. In V. Kurkova-Pohlova and J. Koutnik, editors, Artificial Neural Networks – ICANN 2008, pages 513–522. Springer, 2008.
-  M. Lukoševičius and H. Jaeger. Reservoir computing approaches to recurrent neural network training. Computer Science Review, 3(3):127–149, 2009.
-  Yong Zhang, Peng Li, Yingyezhe Jin, and Yoonsuck Choe. A digital liquid state machine with biologically inspired learning and its application to speech recognition. IEEE transactions on neural networks and learning systems, 26(11):2635–2649, 2015.
-  A. V. Oppenheim, R. W. Schafer, and J. R. Buck. Discrete-time signal processing. Prentice-hall, 1989.
A. Tavanaei, M. T. Manzuri, and H. Sameti.
Mell-scaled discrete wavelet transform and dynamic features for
persian phoneme recognition.
IEEE Symposium on Artificial Intelligence and Signal Processing, pages 138–140, Tehran, Iran, June 2011.
-  E. M. Izhikevich. Simple model of spiking neurons. IEEE Transactions on Neural Networks, 14(6):1569–1572, 2003.
-  D. Pearce and H. G. Hirsch. The Aurora experimental framework for the performance evaluation of speech recognition systems under noisy conditions. In Automatic Speech Recognition: Challenges for the New Millenium, pages 181–188, Paris, France, 2000.
-  Jonathan D Victor and Keith P Purpura. Metric-space analysis of spike trains: theory, algorithms and application. Network: computation in neural systems, 8(2):127–164, 1997.
-  Jonathan D Victor. Spike train metrics. Current opinion in neurobiology, 15(5):585–592, 2005.
-  George R Doddington and Thomas B Schalk. Computers: Speech recognition: Turning theory to practice: New ics have brought the requisite computer power to speech technology; an evaluation of equipment shows where it stands today. IEEE spectrum, 18(9):26–32, 1981.