This paper builds a model of predicting the rating of the University on the basis of a neural network in IBM SPSS Statistics. The choice is due to the fact that the program contains gradient descent error function, which is able to automatically configure the network for data classification. The authors describe the modeling technique, a step-by-step algorithm for selecting the architecture of the network, setting its parameters, training and testing. Experiment data of 1102 Russian universities and 123 indicators of their activity was used for this experiment. A vector was supplied as an input for the network, the coordinates of which were the average total score of each University. Indicators were considered independent variables. 30 out of 123 indicators were left for the study by the method of correlation analysis. The number of input neurons was equal to the number of independent variables. The output layer contained the amount of neurons equal to the number of dependent variables. The activation function of neurons in the hidden and output layer is sigmoid. The authors present the results of modeling. Using the constructed model, the input data was divided into clusters: “eficient”, “ineficient”. Centers of clusters were determined. The sample was split for two network architectures with diferent number of layers and neurons. The percentage of error on the control and training samples was calculated. Quality of the proposed model was evaluated using ROC (Receiver Operating Characteristic) curve.
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In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the VIII Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”, Moscow, Russia, 20-Apr-2018, published at http://ceur-ws.org
To build the prediction model, a large dataset with various dimensions was used
(Table 1). In statistical methods of data processing it does not matter how the objective
function’s residual is minimized [
The advantages of neural network modeling include the ability to work with data
with diferent measurement scales and the possibility of approximating any continuous
function [
The implementation of the model through a neural network can be performed using various programs. The authors selected IBM SPSS Statistics 25 because of their commercial availability.
The object of research is the performance indicator of Russian universities. The subject of the study is the process of predicting the rating of the university.
The aim of the research is the methodological aspects of constructing a neural network model for predicting the rating of the university using the tools – the IBM SPSS package.
The scientific novelty of the research consists in the development of methods and
algorithms for analyzing and predicting the evaluation of the activity of the university
with the use of neural networks [
The work is of practical importance, since it contains a methodology for constructing
a model and setting up a multilayer perceptron in the IBM SPSS Statistics [
The initial data for modeling is presented in Table 1. Objects of the study are 1102 Russian universities. This sample includes all state universities and private higher education institutions head units of the Moscow region. Properties of objects – 123 indicators of the work of universities.
For example:
I.1.1 (Average score of the Unified State Examination of students, accepted according to the results of the Unified State Examination for full-time education according to the bachelor’s and specialist programs at the expense of the corresponding budgets of the budget system of the Russian Federation, point);
I.2 (The average score of USE students of the University, taken according to the results of the USE for full-time education under the Bachelor’s and Specialist programs at the expense of the corresponding budgets of the budget system of the Russian Federation, with the exception of people who have entered special rights and within the quota of the target admission, score);
I.2.16 (Number of grants received for the reporting year per 100 NDP, units); 10 (Total amount of R & D performed by own forces, thousand rubles); 11 (The total amount of work, services related to scientific, scientific and technical, creative services and development, made by own forces, thousand rubles); 12 (Total number of publications of the organization per 100 NDP, units); 13 (Number of business incubators, units); 14 (Number of technoparks, units); 15 (Number of centers for collective use of scientific equipment, units); 16 (Number of small enterprises, units); 17 (Total number of post-graduate students, people); 18 (The proportion of post-graduate students studying in full-time,%). Table 1 has the headings: “Name”, “Results of performance evaluation”, “Scorecard”: – References; – Name of the educational organization; – Region; – Departmental afiliation; – Website; – Organization profile; – Information about the parent educational organization; – Name of the educational organization; – Region.
3.
Based on these indicators, to predict the value of the target binary variable — whether the work of the university will be efective. Using the IBM SPSS Statistics, build a neural network that divides the input data into clusters and identifies their centers. According to the trained network, determine to which cluster the new input vector will belong.
The input vector (dependent variables) is the average total score collected by the institution. Independent variables (factors) are indicators (“Results of performance evaluation”) that have been coded for ease of presentation in the table in accordance with program requirements, for example:
P.1. – Educational activity; P.2. – Scientific-research activity; P.3. – International activity; P.4. – Financial and economic activity; P.5. – Salary of the teaching staf; P.6. – Employment.
4.
For modeling, the multilayer perceptron network architecture was used [
Stages of building a network: – assess the significance of the indicators and determine the range of change in their values; – prepare data for modeling; – design the network architecture – determine the number of layers and the number of neurons in each layer; – training; – testing. 5.
Before the simulation, the data was checked for abnormal emissions in values,
duplicates were deleted, etc. [
Since the experimental sample is large, it was dificult to construct a histogram taking any form. Therefore, the nature of data distribution was determined by a graphical method: construction of quantile graphs (Fig. 1). The graph shows the quantiles of two distributions – empirical (i.e. based on the analyzed data) and theoretically expected standard normal distribution. The quantiles are lined up at an angle of 450. Based on this, the authors concluded that the distribution of the studied data is normal.
More details of this important phase of the analysis are not described in the article.
At the stage of preliminary data preparation, 30 were left for the study in order to reduce the sample size by correlation analysis from 123 indicators.
A hyperbolic tangent or sigmoid function is usually used as an activation function. Activation function is a function that calculates the output signal of an artificial neuron. Sigmoid – is an increasing everywhere diferentiable s-shaped nonlinear function with saturation, which allows you to amplify weak signals without saturating with strong signals. The activation function decides on the activation of the neuron and makes it easier to train the network with the method of reverse propagation of the error.
In the preparation of quantitative variables, the domain of definition and the value of
the activation function were taken into account. The activation function – the sigmoid
has the range of values (0, 1) [
The number of neurons of the input layer of the network is equal to the number of independent variables — 30. Each dependent variable is assigned to one output neuron. The number of hidden layers is determined automatically by SPSS. The activation function of the neurons of the hidden and output layer is the sigmoid.
In order to assess the accuracy of the constructed model, part of the sample from training was deleted. Thus, the data was divided into three parts in proportion: 60% — training, 20% — control and 20% — test. The control sample served to estimate the accuracy, and the test sample demonstrated the operation of the neural network for clustering data. The separation was done randomly by the program. The learning control took place in a mini-packet mode, in which the algorithm for back propagation of the error is a stochastic gradient descent. Rule for stopping network learning: the maximum number of steps without changing the error. The parameters “interval center” and “interval ofset”, which set the range of initial values of the weights of the neural network, were taken equal to 0 — the center of the interval, and the ofset from 0.5 to 1.5.
6.
The number of hidden layers and the number of neurons in these layers was selected automatically by the program, two models with diferent network architectures were built (Table 2).
Neural network models with diferent architectures
Results of the classification
Predicted 1 cluster
2 cluster 56.9% 56.8% 56.2% 43.1% 43.2% 43.8%
Using the ROC (Receiver Operating Characteristic) curve, you can estimate the quality of the constructed model. The diagonal line in the graph (Fig. 2) is the indicators of the lack of informative model. The more the curve is bent the better the network is trained. It is considered that the coeficient of the area of the curve in the range 0.9–1.0 indicates a very good quality of the model. As a result of constructing the neural network the indicator reached 0.97.
As for the interpretation of the model for the experimental data, the results of partitioning into clusters using a neural network matched with experimental observations.
17.9% 18%
Calculations showed that the number of layers and neurons do not greatly afect the quality of the model. As a result of the study, the sample was divided into two clusters (Table 3). The percentage of errors on the training and control samples is almost the same, which indicates a well-trained network. The first cluster of “efective university” included all public and private institutions of higher education that carried out 4 or more monitoring indicators.
The authors considered the methodology for modeling the rating of universities by
the example of building a neural network in the IBM SPSS Statistics. This technique can
be an alternative to statistical methods for studying similar experimental data [