The paper presents research on the problem of recognition of signs applied to the analysis of basic units of ancient Russian chants. For testing, we take two types of deep neural networks: Back Propagation Neural Network (BPNN) and Convolution Neural Network (CNN). We investigate main features of the chant units and the properties of the networks to choose the best structure and algorithm. The results provide an analysis of accuracy for both approaches used in solving this particular task.
One of the most important and prominent tasks in the study of ancient Russian culture is the exploration of melodic content in vocal music manuscripts from the XII-XVII centuries. The melodies in these books are written using special musical structures that evolved in Russia over the centuries. The concept «semiography» is understood to mean the conventionally accepted methods of musical writing and expression of certain musical sounds and how they are related. Fig. 1 shows a fragment of a semiographic chant.
Music chants written by Znamenny Notation contain rows of semiographic
signs (znamyas, flags) and rows of words divided by syllables. Every semiographic
sign has special type of marks “Pometa”. These marks indicate the duration
and amplitude of the music [
There are seven most common types of pometas (see Table 1). Dataset is generated by our program and includes 488 images. It was randomly divided into 2 separate sets: training and test. The training set had 70 percents of the examples and the remaining 30 persents formed test set. Program automatically cuts pometas from full image. Fig. 2 shows how program handles fragment of image. At first the program cuts the characters using an algorithm developed by us. The essence of the algorithm is to extract the image area and calculate standard deviation3in this area. If the value is greater than the value specified by us on the next layer of all the pixel values fall, if not then the next layer gets nothing. After this treatment, there is a noise that is removed by another algorithm is based on identifying the character contour. If the character contour size more than a certain value, pixels inside the contour fall to the next layer.
The table below presents the number of examples of each type in the training and test sets.
For our neural networks, we create program to convert images from JPG format to “MNIST”4 one. MNIST is a simple computer vision dataset on which are
Standard-Deviation-from-Channels-Statistics/
based the recognition problem. The current best error rate on the MNIST
digitnumberrecognition task (<0.3) approaches human performance [
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Pixels are organized row-wise. For our experiments we have used pixels with values from 0 to 255. 0 means background (white), 255 means foreground (black).
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In this article used the computer with 8GB Ram DDR3 on which the OS Microsoft Windows 8.1 and OS Ubuntu 15.04 is installed. It has a processor Intel Core i7-970 and videocard Radeon R280x. Also, for a machine learning used library known as TensorFlow6. Using TensorFlow makes it easy to implement backpropagation for convolutional neural networks, since it automatically computes all the mappings involved. It is also quite a bit faster than other libraries, and this makes it practical to train more complex networks. In particular, one great feature of TensorFlow is that it can run code on either a CPU or, if available, a GPU. Running on a GPU provides a substantial speedup and, again, helps make it practical to train more complex networks. alculations are performed without using the GPU and computing time is less than 10 minutes. 3
The structure of our BPNN7 is described in fig. 3. Our net consists of three layers: an input layer, a hidden layer and an output layer. The input layer has 784 units, or neurons. Hidden layer has 625 and the output 7 units.
The standard way to model a neuron’s output f as a function of its input x is
with f (x) = tanh(x). In terms of training time with gradient descent, these
saturating nonlinearities are much slower than the non-saturating nonlinearity f(x)
= max(0, x). Following Nair and Hinton [
with ReLUs train several times faster than their equivalents with tanh units.
Two additional major benefits of ReLUs are sparsity and a reduced likelihood of
vanishing gradient. One major benefit is the reduced likelihood of the gradient
to vanish. This arises when a>0. In this mode, the gradient has a constant value.
In contrast, the gradient of sigmoids becomes increasingly small as the absolute
value of x increases. The constant gradient of ReLUs results in faster learning.
The other benefit of ReLUs is sparsity. Sparsity arises when a<=0. The more
such units that exist in a layer the more sparse the resulting representation.
Sigmoids on the other hand are always likely to generate some non-zero value
resulting in dense representations. Sparse representations seem to be more
beneficial than dense representations. We are not the first to consider alternatives
to traditional neuron models in CNNs. For example, Jarrett et al. [
of input features to the fully connected layers. After about two or three layers the accuracy gain becomes rather small so we need to decide what is more important: generalization accuracy or training time. All image recognition tasks are different so the best method is to simply try incrementing the number of convolutional layers one at a time until we are satisfied by the result.
Second parameter is the number of hidden layers. The number of required hidden layers depends on the intrinsic complexity of dataset, this can be understood by looking at what each layer achieves: – Zero hidden layers allow the network to model only a linear function. This is unsuitable for most image recognition tasks. – One hidden layer allows the network to model an arbitrarily complex function. This is suitable for nearly all image recognition tasks. – Theoretically, two hidden layers offer little benefit over a single layer, however, in practice especially complex tasks may find an additional layer beneficial. This should be treated with caution, as a second layer can cause over-fitting. Using more than two hidden layers is almost never beneficial9.
Third parameter is the number of nodes per hidden layer. There is no formula for deciding upon the number of nodes, it is different for each task. A rough guide to go by is to use a number of nodes 2/3 the size of the previous layer, with the first layer 2/3 the size of the final feature maps. This however is just a rough guide and depends again on the dataset. Another commonly used option is to start with an excessive number of nodes, then to remove the unnecessary nodes through pruning. For better recognize images input layer has padding.
Fourth parameter is the numbers of pooling layers. Pooling layers in CNNs
summarize the outputs of neighboring groups of neurons in the same kernel map.
Traditionally, the neighborhoods summarized by adjacent pooling units do not
overlap (e.g.,[
Combining the predictions of many different models is a very successful way to
reduce test errors [
As we can see, CNN and BPNN have more answers that are correct but to obtain this result the network needs more time to train, because they have more parameters to train. Table 5 shows accuracy per each pometa.
So as we can see accuracy of pometas "H" and "П" only are different from one. This can be explained by the fact that they are very similar. During our research, we have developed two algorithms to processing image and compared four types of neural networks. We have achieved excellent accuracy image recognition. So our program itself can define pometas and translate them into a digital format. Further it is possible to improve and to determine not only the pometas but also others symbols. This program is easy to understand because there are not so many parameters to change.