![Artificial Neural Network
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Artificial neural network (ANN) is an artificial intelligence
model originally designed to replicate the human brain’s
learning process.
Step 1. Calculating the weighted sum and adding a bias
term, δj according to equation 1:
( ) = for = 1, 2,…, ...(1)
Step 2. Transforming the f(net)j through a suitable
mathematical transfer function or activation function, and
Step 3. Transferring the result to neurons in the next layer.
Transformation Functions:
1]g(x) = x (Linear function)
2]g(x) = (Sigmoid function)
3]g(x) = (Hyperbolic tangent function)](https://image.slidesharecdn.com/estimateofhousepriceusingstatisticalandneuralnetworkmodel-180807095342/85/Estimate-of-house-price-using-statistical-and-neural-network-model-5-320.jpg)
Estimate of house price using statistical and neural network model
- 1. Yashwantrao Chavan Institute of Science, Satara A Research paper on: Comparative Study On Estimate House Price Using Statistical And Neural Network Model. ( Azme Bin Khamis, Nur Khalidah Khalilah Binti Kamarudin) Presented By: Patil Shweta Satappa M.Sc II Roll No. 215
- 3. Introduction Housing market is of great important for the economy activities. Housing construction and renovation boost the economy through an increase in the aggregate expenditures, employment and volume of house sales. Traditional house price prediction is based on cost and sale price comparison lacking of an accepted standard and a certification process. Therefore, the availability of a house price prediction model helps fill up an important information gap and improve the efficiency of the real estate market. Recent studies further justify the necessity of housing price analysis with a conclusion that housing sector plays a significant role in acting as a leading indicator of the real sector of the economy and assets prices help forecast both inflation and output. House prices have a strong link with both income and interest rates. Artificial neural network has been limitedly used for valuation or forecasting property price, studies carried out to compare the accuracy of linear regression and artificial neural network discovered that the latter has superiority compared to the former. compared linear regression and artificial neural network in predicting housing value used artificial neural network and compared its accuracy with that of linear regression in predicting of housing price. This study aimed to compare between MLR model and Neural Network model to predict the house prices in New York. Secondary data from 1047 houses in New York is used in artificial neural network to predict the house price
- 4. Research Methodology • • • • • Multiple Linear Regression: The model for Multiple Linear Regression can be represented as: ( / ) = 0+ 1 1+⋯+ where β0= intercept βj= slopes or regression coefficients. = SST = SSR = R2 = 1 - R2 adj = 1 - Ftest =
- 5. Artificial Neural Network • • • • • Artificial neural network (ANN) is an artificial intelligence model originally designed to replicate the human brain’s learning process. Step 1. Calculating the weighted sum and adding a bias term, δj according to equation 1: ( ) = for = 1, 2,…, ...(1) Step 2. Transforming the f(net)j through a suitable mathematical transfer function or activation function, and Step 3. Transferring the result to neurons in the next layer. Transformation Functions: 1]g(x) = x (Linear function) 2]g(x) = (Sigmoid function) 3]g(x) = (Hyperbolic tangent function)
- 6. General structure of a neural network with input layer, two hidden layers and output layer
- 7. Learning Process: • • • • • Training is formed by a vector X(inp)= (Xi1, Xi2,………, Xim) of inputs and a vector Y(out)=(Yi1, Yi2,………., Yin) of outputs. The objective of the training process is to approximate the function f between the vectors X(inp) and the Y(out), Y(out) = f(X(inp)). One of the functions most commonly used is the sum-of squared residuals E= (Yij - Yij *)2 ………..(2) where yij and yij* are the actual and network’s jth output corresponding to the ith input vector, respectively. The current weight change on a given layer is given by equation (3) : ∆Wij= -η(dE/dWij) ………(3) where η is a positive constant called the learning rate. To achieve faster learning and avoid local minima, an additional term is used and equation (3) becomes: ∆Wk ij= η(dE/dWij) + μ ∆Wk-1 ij where μ is the “momentum” term and ∆Wk-1 ij is the change of the weight Wij from the (k-1)th learning cycle.
- 8. Data Analysis • • • • • • Regression Analysis: The relationship between dependent variable with independent variables was performed using Pearson correlation. Let, Y= House Price X1 =living area X2 =Bathroom X3 =Bedroom X4 = Fireplace X5 = Age of house r(Y, X1 )= 0.776 r(Y, X2 )=0.670 r(Y, X3 )=0.471 r(Y, X4 )=0.460 r(Y, X5)= -0.363 Consider , MLR model, Yˍ= X1β1 + X2β2 + X3β3 + X4β4 + X5β5 +ε ε ̴iid N(0,σ2) Hypothesis: H0 = βj =0 j=1,2,… 5 (Effect of regression coefficient is not significant.) The regression equation for the house price can be written as follow; House price(Y) = 27467.001 + 67.211*X1 + 16,402.244*X2+ – 5167.260*X3 +10, 099.817*X4 – 216.718*X5 F statistic is 380.696 and p-value is 0.0000, means that the model is suitable and can be fitted to the data. The coefficient of determination R2= 0.646 and R2 adj = 0.645, it shows that 64.5%
- 10. Artificial Neural Network The number of nodes or neurons in hidden layer are determined by trial and error process. We starts our trial and error with 2 nodes and the process is repeated until 15 nodes. The researcher compares the MSE value and R value for all number of nodes. The lowest MSE value with higher R value will be selected as optimum number of nodes in hidden layer. Number of nodes MSE R Number of nodes MSE R 2 1.574 E9 0.8118 9 1.401 E9 0.8135 3 2.566 E9 0.8215 10 1.293 E9 0.9039 4 1.843 E9 0.8341 11 2.108 E9 0.8845 5 1.443 E9 0.8378 12 1.507 E9 0.8752 6 1.468 E9 0.8563 13 1.433 E9 0.8588 7 1.476 E9 0.8665 14 1.434 E9 0.8231 8 1.476 E9 0.8239 15 1.499 E9 0.8025
- 11. Based on Table, the lowest MSE value is 1.293E9 with 10 nodes in hidden layer and correlation coefficient is 0.9039. Hence, 10 nodes are selected as optimum number of nodes in hidden layer.
- 12. Result • • • • The value of R2 and MSE for MLR model is 0.644 and 1.633E9. The value of R2 and MSE for Neural Network model is 0.817 and 1.293E9. The R2 value for Neural Network model is higher compared to MLR model. The value of MSE in Neural Network model is lower compared to MLR model. Therefore, Neural Network model is preferred to predict house price.
- 13. Conclusion • • • • The model’s accuracy in predicting house price was measured by a number of criteria. The value of R2 and MSE were compared to select preferred model. By using ANN, the R2 value was increase about 26.475% higher than MLR. It can be conclude Neural Network model is preferred to predict house price compared to MLR model and can be used as an alternative way to estimate house price in future.
- 14. References • • www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 12, December 2014 ISSN 2277-8616 ( Azme Bin Khamis, Nur Khalidah Khalilah Binti Kamarudin)
- 15. Thank You….