APPLICATION OF A MULTI- LAYER PERCEPTRON FOR MASS VALUATION OF REAL ESTATES

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FIG WORKING WEEK 2008 APPLICATION OF A MULTI- LAYER PERCEPTRON FOR MASS VALUATION OF REAL ESTATES Tomasz BUDZYŃSKI, PhD Artificial neural networks the highly sophisticated modelling technique, which allows project functions of a very high level of complexity

Architecture of the multi-layer perceptron Teaching the multi-layer perceptron software routines which simulate activities of neural networks not programmed, rather taught (trained) using various examples examples: features of real estates, selling prices, the level of rent.

Teaching the multi-layer perceptron processing of input data (examples) successive passes of series of data through the multi-layer perceptron result in adjustment of weights of particular connections and threshold values of the neurone, in such a way, that differences between the results of work of the network (the real estate value) and the expected result (the real estate price) are minimised The multi-layer perceptron design the number of hidden layers the number of neurones in particular layers

Training of the multi-layer perceptron the stage of teaching the stage of testing the stage of analysis of results Teaching the multi-layer perceptron teaching algorithms the back propagation of errors algorithm (BP) the conjugate gradient descent algorithm(cg) the quasi-newton algorithm (QN) the Levenberg-Marquardt algorithm (LM)

Investigations Accuracy of determination of real estate values using the multi-layer perceptron taught by means of four mentioned above teaching algorithms Investigations data of 114 transactions of land, non-built-up parcels, planned for one-family houses, located in Otwock choice of features which in the essential way influence the price level of land on the local real estate market construction of ANN models

Choice of features features location neighbourhood technical infrastructure access to public transport parcel size state of developing methods the genetic algorithm the backward step method Construction of ANN models All transactions were divided into: the teaching subset 71 cases, the validation subset 29 cases, the testing subset 14 cases. Those subsets have similar statistical characteristics: the mean value 60,00 zł/m2 and 60,44 zł/m2, 59,77 zł/m2, the standard deviation values 31,27 zł/m2 and 33,31 zł/m2, 30,35 zł/m2

Construction of ANN models Architecture of a multi-layer perceptron - 3, 4, 5 hidden neurones Teaching algorithms back propagation of errors conjugate gradient descent quasi-newton Levenberg-Marquardt The total of 1200 multi-layer perceptrons were created. Number of hidden neurones Error in teaching subset zł/m 2 Error in validation subset zł/m 2 Error in testing subset zł/m 2 3 9,696718 10,49435 11,76747 BP 97 4 9,643689 10,59871 11,31541 BP 99 5 9,584256 10,36612 11,35798 BP 92 3 8,553579 9,317702 9,744248 CG 99 4 8,896472 9,180777 11,35737 CG 96 5 8,047045 9,097722 10,67246 CG 99 3 8,577321 9,251484 10,44241 QN 92 4 8,996874 9,058687 10,02242 QN 86 5 8,054216 9,437988 10,88689 QN 80 3 7,973481 8,838693 11,05852 LM 95 4 7,460221 8,534605 10,97577 LM 94 5 7,550017 8,587820 9,388863 LM 28 Teaching algorithm, number of teaching epoch

Conclusions Out of investigated teaching algorithms, the Levenberg-Marquardt algorithm allows to construct the best multi-layer perceptron, i.e. the perceptron characterised by the smallest value of the error in the validation subset.

Conclusions The conjugate gradient (CG) and the quasi- Newton algorithms allow to achieve lower accuracy of determination of real estate values. The back propagation of errors algorithms (BP) turned to be characterised by the lowest efficiency, comparing to other investigated algorithms. Conclusions Those conclusions concern the network of architecture of low complexity level, which consist of several input neurons, several hidden neurons and one output neuron, i.e. the networks constructed for the needs of determination of real estate values.

Conclusions Differences in the intensity of teaching the multi-layer perceptron by means of various teaching algorithms for the network of low architectural complexity using about 100 examples become unimportant. Conclusions Increase of the number of hidden neurones in the multi-layer perceptron not always results in decrease of the value of the error of determination of a real estate value. In the case of teaching the neural network using the Levenberg-Marquardt (LM) and the quasi-newton (QN) algorithm the error in the validation subset for the network with 5 hidden neurons was greater than the same error in the network with four neurons in the hidden layer.

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