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Artificial intelligence neural computing and regression methods for shelf life prediction of kalakand Sumit Goyal1 and Gyanendra Kumar Goyal2 Dairy Technology Division, National Dairy Research Institute, Karnal-132001 (Haryana), India Abstract Kalakand or Qalaqand is a popular Indian sweet made out of solidified, sweetened milk and cottage cheese. It owes it origin to the milk-rich Braj area of western Uttar Pradesh. It is a very popular sweetmeat in North and East India, including Jharkhand, Orissa and Bengal and is reputed for its exquisite taste. The term qand in qalaqand is derived from the Arabic language and means sweets. Artificial neural networks have been developed as generalizations of mathematical models of biological nervous systems. Cascade Computing, Generalized Regression and Multiple Linear Regression artificial intelligence models for shelf life prediction of Kalakand were developed. The results of models were evaluated with three types of prediction performance measures viz., Mean Square Error , Root Mean Square Error and coefficient of determination R2.The best result for cascade computing model with single hidden layer (MSE 0.000592818; RMSE: 0.024347850; R2: 0.992884381),for double hidden layer best results(MSE 0.000592818; RMSE: 0.02434785; R2: 0.992884381).Best results for generalized regression were (MSE 0.001152787; RMSE: 0.033952711; R2: 0.986166561) and for multiple linear regression (MSE 0.000144005; RMSE: 0.0120002; R2: 0.998271839). From the investigation, it can be concluded that the multiple linear regression model has better than cascade and generalized regression models in predicting shelf life of buffalo milk Kalakand stored at 6oC. Keywords: Artificial intelligence, Cascade, Generalized Regression, Multiple Linear Regression, Kalakand Present address: 1Senior Research Fellow (Corresponding author: [email protected]), 2Emeritus Scientist, 1, 2 National Dairy Research Institute, Karnal-132001 (India). Artificial intelligence neural computing and regression methods for shelf life prediction of kalakand 1. Introduction Kalakand or Qalaqand is a popular Indian sweet made out of solidified, sweetened milk and cottage cheese. It owes it origin to the milk-rich Braj area of western Uttar Pradesh. It is a very popular sweetmeat in North and East India, including Jharkhand, Orissa and Bengal and is reputed for its exquisite taste. The term qand in qalaqand is derived from the Arabic language and means sweets [1]. The human brain provides proof of the 1 existence of massive neural networks that can succeed at those cognitive, perceptual, and control tasks in which humans are successful. The brain is capable of computationally demanding perceptual acts (e.g. recognition of faces, speech) and control activities (e.g. body movements and body functions).The advantage of the brain is its effective use of massive parallelism, the highly parallel computing structure, and the imprecise information-processing capability. The human brain is a collection of more than 10 billion interconnected neurons. Treelike networks of nerve fibers called dendrites are connected to the cell body or soma, where the cell nucleus is located. Extending from the cell body is a single long fiber called the axon, which eventually branches into strands and substrands, and are connected to other neurons through synaptic terminals or synapses. The transmission of signals from one neuron to another at synapses is a complex chemical process in which specific transmitter substances are released from the sending end of the junction. The effect is to raise or lower the electrical potential inside the body of the receiving cell. If the potential reaches a threshold, a pulse is sent down the axon and the cell is ‘fired’. Artificial neural networks (ANN) have been developed as generalizations of mathematical models of biological nervous systems. A first wave of interest in neural networks (also known as connectionist models or parallel distributed processing) emerged after the introduction of simplified neurons by McCulloch and Pitts (1943). The basic processing elements of neural networks are called artificial neurons, or simply neurons or nodes. In a simplified mathematical model of the neuron, the effects of the synapses are represented by connection weights that modulate the effect of the associated input signals, and the nonlinear characteristic exhibited by neurons is represented by a transfer function. The neuron impulse is then computed as the weighted sum of the input signals, transformed by the transfer function. The learning capability of an artificial neuron is achieved by adjusting the weights in accordance to the chosen learning algorithm. A neural network has to be configured such that the application of a set of inputs produces the desired set of outputs. Various methods to set the strengths of the connections exist. One way is to set the weights explicitly, using a priori knowledge. Another way is to train the neural network by feeding it teaching patterns and letting it change its weights according to some learning rule. The learning situations in neural networks may be classified into 2 three distinct sorts. These are supervised learning, unsupervised learning, and reinforcement learning. In supervised learning, an input vector is presented at the inputs together with a set of desired responses, one for each node, at the output layer. A forward pass is done, and the errors or discrepancies between the desired and actual response for each node in the output layer are found. These are then used to determine weight changes in the net according to the prevailing learning rule. The term supervised originates from the fact that the desired signals on individual output nodes are provided by an external teacher [5]. 1.1 Cascade Computing (CC) Model The ideas behind the cascade-correlation architecture are as follows. The first is to build up the cascade architecture by adding new neurons together with their connections to all the inputs as well as to the previous hidden neurons. This configuration is not changed at the following layers. The second idea is to learn only the newly created neuron by fitting its weights so that to minimize the residual error of the network. The new neurons are added to the network while its performance increases. So, the common cascade-correlation technique assumes that all m variables x1,…, xm characterizing the training data are relevant to the classification problem. At the beginning, a cascade network with m inputs and one output neuron starts to learn without hidden neurons. The output neuron is connected to every input by weights w1,…, wm adjustable during learning. The output y of neurons in the network is given by the standard sigmoid function f. Then the new neurons are added to the network one-by-one. Each new neuron is connected to all m inputs as well as to all the previous hidden neurons. Each time only the output neuron is trained. For training, any of algorithms suitable for learning a single-neuron can be used. Training a new neuron, the algorithm adjusts its weights so that to reduce the residual error of the network. The algorithm adds and then trains the new neurons while the residual error decreases. The advantages of the cascade neural networks are well known. First, no structure of the networks is predefined, that is, the network is automatically built up from the training data. Second, the cascade network learns fast because each of its 3 neurons is trained independently to each other. However, a disadvantage is that the cascade networks can be over-fitted in the presence of noisy features [2]. 1.2 Generalized Regression (GR) Model Generalized regression models are a kind of radial basis network that are used for function approximation. Syntax: net = newgrnn (P,T,spread) net = newgrnn(P,T,spread) takes three inputs, P: R-by-Q matrix of Q input vectors T: S-by-Q matrix of Q target class vectors Spread : Spread of radial basis functions (default = 1.0) and returns a new generalized regression model. To fit data very closely, use a spread smaller than the typical distance between input vectors. To fit the data more smoothly, use a larger spread. Larger the spread, the smoother the function approximation. Newgrnn creates a two-layer neural network. The first layer has radbas neurons in it and calculates weighted inputs with dist and net input with netprod. The second layer has purelin neurons, calculates weighted input with normprod, and net inputs with netsum. Only the first layer has biases. newgrnn sets, the first layer weights to P', and the first layer biases are all set to 0.8326/spread, resulting in radial basis functions that cross 0.5 at weighted inputs of +/– spread. The second layer weights W2 are set to T [3]. 1.3 Multiple Linear Regression (MLR) Regression reveals average relationship between two variables and makes possible to predict the yield. In mathematics Y is called a function of X, but in Statistics it is termed as regression which describes relationship. Hence, regression is the study of functional relationship between two variables of which one is dependent (Y) and other is independent (X). Regression analysis provides an estimate of values of the dependent variable from values of the independent variable. This estimation procedure is called the regression line. Regression analysis gives a measure of the error. With the help of regression coefficients we can find the value of correlation coefficient. The multiple regression analysis gives the best linear prediction equation involving several 4 independent variables. It also helps in finding the subset that gives the best prediction values of Y. The multiple regression equation describes the average relationship between dependent and independent variables which is used to predict the dependent variable. If Y depends partly on X1 and partly on X2 then the population regression equation is written as, YR 1 X 1 2 X 2 , Eq. (1) 1 measures the average change in Y when X1 increases by 1 unit, X2 remaining unchanged it is called the partial regression coefficient of Y on X1 and 2 the partial regression coefficient of Y on X2 which measures the average change in Y when X2 increases by 1 unit, X1 remaining unchanged. Thus the regression model is Y 1 X 1 2 X 2 , Eq. (2) where, N (0, 2 ) [4]. ANN has been successfully applied for predicting food quality [6], odor change of muscadine grape [7], fruit ripening [8].There has been no research till date on predicting shelf life of Kalakand. 2. Method Materials Fig.1 Design of neural network 5 The input parameters for models were tyrosine, moisture, free fatty acids, titratable acidity, peroxide value and sensory score was output parameters which are displayed in Fig.1. Kalakand datasets were developed at National Dairy Research Institute, Karnal, (India). The dataset consisted of 60 live observations. Further, the dataset was divided into two subsets i.e., 48 data observations (80% of data observations) were used for training the network and 12 for testing (20% of data observations) the network. CC, GR and MLR models were developed and compared with each other for shelf life prediction of Kalakand. The network was trained with upto 500 epochs and number of neurons in single and double hidden layers varied from 1 to 30 , different combinations were tried and tested , as there is no predefined rule of achieving good results other than hit and trail method. As the number of neurons increased as the training time. There are two problems that were kept in mind while training the network, problem of overfitting and problem of underfitting .Overfitting means that the size of neurons used in training the network should not be large, as it is difficult for the network to train and underfitting means neurons should not be less as it is difficult for a neural network to get properly trained .Hence, balance must be maintained, while training the neural network. The Neural Network Toolbox under MATLAB 7.0 software was used for development of artificial intelligence computing models. Different algorithms were tried i.e., Fletcher-Powell Conjugate Gradient(traincgf), Levenberg-Marquardt (trainlm), BFGS Quasi-Newton (trainbfg), Bayesian Regularization (trainbr), Resili Backpropagation(trainrp), Scaled Conjugate Gradient (trainscg), Conjugate Gradient with Powell/Beal Restarts( traincgb), PolakRibiére Conjugate Gradient( traincgp), One Step Secant( trainoss) Variable Learning Rate Backpropagation (traingdx ). Bayesian regularization gave good results, therefore it was selected as the training algorithm for the neural network. Performance measures for prediction N Q Q exp cal MSE n 1 2 1 N Qexp Qcal RMSE n 1 Qexp 6 2 Eq. (3) Eq. (4) N Q Q exp cal R 1 2 1 Qexp 2 2 Eq. (5) Q exp = Observed value; Qcal = Predicted value; n = Number of observations in dataset. 3. Results and Discussion Table 1. Results of experiments for CC model with single hidden layer Neurons in Hidden Layer MSE RMSE R2 3 4 5 7 10 12 15 17 20 25 30 0.009680652 0.000592818 0.009290401 0.001279354 0.001661461 0.003712751 0.001024186 0.001324841 0.002385685 0.00284096 0.003515725 0.098390304 0.024347850 0.096386725 0.03576806 0.040761019 0.060932351 0.032002906 0.036398359 0.048843471 0.053300653 0.059293547 0.883087967 0.992884381 0.887656189 0.984634092 0.980062472 0.955446983 0.987699195 0.984101914 0.971371784 0.965908485 0.940706453 Table 2. Results of experiments for CC model with two hidden layer Neurons in Hidden Layer MSE RMSE R2 2:2 3:3 5:5 6:6 7:7 8:8 10:10 12:12 15:15 18:18 20:20 0.000592818 0.001401085 0.012070402 0.008092429 0.008489083 0.004769402 0.003249304 0.001467108 0.001705251 0.000994657 0.00098877 0.02434785 0.03743107 0.10986538 0.089957932 0.092136219 0.069060856 0.05700267 0.038302848 0.041294684 0.031538184 0.031444715 0.992884381 0.983171243 0.854086061 0.902073957 0.897210554 0.942595717 0.960897045 0.982368529 0.979507173 0.988058022 0.988125331 7 Table 3. Results of experiments for GR model Spread Constant MSE RMSE R2 2 3 4 5 6 7 8 9 10 25 40 0.001152787 0.002836909 0.005046995 0.006850000 0.008135249 0.009032628 0.009667907 0.010129284 0.010471581 0.011789805 0.011952980 0.033952711 0.053262638 0.071042204 0.082764727 0.090195614 0.095040137 0.098325516 0.100644342 0.102330745 0.108580870 0.109329685 0.986166561 0.965957096 0.939436063 0.917799999 0.902377015 0.891608467 0.883985114 0.878448597 0.874341023 0.858522335 0.856564239 Table 4. Result of Regression Model Regression Model MLR MSE RMSE R2 0.000144005 0.0120002 0.998271839 Fig.2 Graphical representation of actual and predicted sensory score for CC model with one hidden layer 8 Fig.3 Graphical representation of actual and predicted sensory score for CC model with two hidden layers Fig.4 Graphical representation of actual and predicted sensory score for GR model 9 Fig.5 Graphical representation of actual and predicted sensory score for MLR model Numerous experiments were carried with CC, GR and MLR models. Different combinations were tried, tested and compared with each other as represented in the tables 1, 2, 3 and 4 respectively. CC models with single hidden layer having four neurons gave the best outcome (MSE 0.000592818; RMSE: 0.024347850; R2: 0.992884381). CC models with two hidden layers having two neurons in the first layer and two neurons in the second layer gave best result as (MSE 0.000592818; RMSE: 0.02434785; R2: 0.992884381). GR model was also developed, the best results given by this model with spread constant as 2 are (MSE 0.001152787; RMSE: 0.033952711; R2: 0.986166561).Statistical model of MLR was developed to compare performance of artificial intelligence neural computing models, it displayed the finest results, (MSE 0.000144005; RMSE: 0.0120002; R2: 0.998271839) as represented in table 5. Table 5. Displaying best results of different models Model Best Results CC single hidden layer model MSE 0.000592818; RMSE: 0.024347850; R2: 0.992884381 CC two hidden layer model MSE 0.000592818; RMSE: 0.02434785; R2: 0.992884381 GR model MSE 0.001152787; RMSE: 0.033952711; R2: 0.986166561 MLR model MSE 0.000144005; RMSE: 0.0120002; R2: 0.998271839 10 Fig.6 Displaying regression equations Hence, MLR model was selected for predicting shelf life of Kalakand by building regressions equations based on sensory scores and constant came out as 8.516, regression coefficient as -0.041 and R2 was found to be 99 percent as represented in fig.6, after solving them 8.25 came as the output which was subtracted from the actual shelf life of the product i.e., 40 days. Hence it was found 31.75 days. 4. Conclusion The possibility of artificial intelligence neural network and statistical computing approach was investigated to predict shelf life of Kalakand. Cascade neural network with single as well as double hidden layers were constructed with generalized regression models and also statistical model of multiple linear regression was developed. Therefore, from the results it can be concluded that statistical computing model of multiple linear regression is superior over cascade and generalized regression models in predicting shelf of buffalo milk Kalakand stored at 6oC. 5. References [1] En.wikipedia.org web-site accessed on 23.5.2011 : “http://en.wikipedia.org/wiki/Kalakand” [2] Arxiv web-site accessed on 24.5.2011 : “http://arxiv.org/ftp/cs/papers/0504/0504067.pdf” [3] Mathworks. web-site accessed on 25.5.2011 : 11 “http://www.mathworks.com/help/toolbox/nnet/ref/newgrnn.html”. [4] S.B. Agarwal, Manual on Statistical Methods for Agriculture and Animal Sciences. Published by National Dairy Research Institute (Deemed University), Karnal 132 001 (Haryana) India, 2010 [5] Softcomputing web-site accessed on 25.5.2011 : “http://www.softcomputing.net/ann_chapter.pdf” [6] G. Xie , R. Xiong , Use of hyperbolic and neural network models in modeling quality changes of dry peas in long time cooking. Journal of Food Engineering. 41 : 151-162, 1999 [7] O. Tokusolu , M.O. Balaban , Evaluation of odor and color changes of muscadine grape stored at different temperatures by electronic nose and computer vision. Abstracts 39B-18 presented at IFT 2000 annual meeting, Dallas, USA, 2000 [8] T. Morimoto, W. Purwanto , J. Suzuki, T. Aono , Y. Hashimoto , Identification of heat treatment effect on fruit ripening and its optimization. In:Mathematical and Control Applications in Agriculture and Horticulture, Munack, A. & Tantau H.J.(Eds.),Oxford: Pergamon Press,267-272,1997 12