KR20120085144A - Multiple linear regression-artificial neural network hybrid model predicting water solubility of pure organic compound - Google Patents

Abstract

PURPOSE: A MLR(Multiple Linear Regression)-ANN(Artificial Neuron Network) mixed model, predicting the water solubility of a pure organic compound, is provided to predict the value of the water solubility even for organic compounds having unknown experimental values, thereby reducing time and cost for an experiment. CONSTITUTION: A molecule descriptor value about the water solubility of a hydrocarbon series organic compound is prepared. Experimental data is separated into a training set and a test set. An optimum MLRM(Multiple Linear Regression Model) for the training set is explored. The predicted performance of the optimum MLRM is tested on the test set. After an optimum ANNM(Artificial Neural Network Model) divides every samples into three sets, it is explored. If the absolute value of the difference of the water solubility prediction value, figured out by the MLRM and the ANNM, is greater than an over-suitability preventing standard value, the water solubility prediction value by the MLRM is selected as a water solubility value.

Description

Multiple Linear Regression-Artificial Neural Network Hybrid Model Predicting Water Solubility of Pure Organic Compound}

The present invention belongs to a field of physical chemistry called physical property prediction and relates to a method for predicting with high accuracy a water solubility, which is one of several physical properties of an organic compound.

Knowing the exact values of the various properties of an organic compound in detail can be used to determine the feasibility of the use of the substance, to design the synthesis and purification processes, and to establish methods and conditions for storage, transport, use, and disposal. It is an important issue both industrially and academically because it is critical to all decision-making processes throughout the process. The most accurate way of knowing the value of the property of interest of an organic compound of interest is also an experiment, but it is true that it is quite costly and time consuming in many aspects, including the preparation of purified samples and the construction of an environment for accurate measurement. Therefore, it may not be possible. Therefore, as an alternative, many researchers have long tried to predict the exact value of various physical properties of organic compounds. As such, the prediction of physical properties has a long history, and new prediction methods are constantly appearing. At present, several prediction models with different accuracy and application range coexist.

Several prediction models have been proposed to date for water solubility, which is a property of interest of the present invention. Water Solubility refers to the maximum mass of solute that can be dissolved in 100 g of water using water as a solvent. The results of previous studies on water solubility prediction are described in David J. Livingstonea, Martyn G. Fordb, Jarmo J. Huuskonenc & David W. Salt, Simultaneous prediction of aqueous solubility and octanol / water partition coefficient based on descriptors derived from molecular structure . Journal of Computer-Aided Molecular Design, 15: 741752, 2001. Currently known and widely used models for predicting water solubility are those that use group contribution methods. Table 1 shows the main group contribution models for water solubility that have been proposed.

year proponent 1992 Klopman & Wang & Balthasar 1995 Kuhne 2001 Klopman & Zhu 2004 Hou & Xia & Zhang & Xu

A typical form of group contribution model is given by

를구하기 위해서는 먼저 값을 알고자 하는 화합물의 분자를 미리 정해진 다수의 조각형식들에 맞추어 쪼갠 다음 각 조각형식들의 개수

를 구한다. 이를 다시 그 형식에 할당된 계수

와곱한 것을 합산한 것이 예측값

가 된다. 계수

들은 실험값이 존재하는 화합물들로부터 모형이 최선의 성능을 갖도록 통계적인 방법을 통해 결정된다.Property value

In order to find the value, first divide the compound of the compound whose value you want to know according to a number of pieces.

. This is again the coefficient assigned to that type

The sum of the squares is the predicted value

Becomes Coefficient

These are determined by statistical methods to ensure that the model has the best performance from the compounds with experimental values.

These group contribution methods have been somewhat successful in the past, but lack the theoretical basis, and sometimes the only way to split them into pieces is not, or even nonexistent, which makes the calculation of values impossible. Also, as the model is improved to improve the predictive performance, it becomes more complicated and difficult to handle.

One of the alternatives to the group contribution method in constructing the prediction model is the QSPR (quantitative structure-property relationship) method. This method basically starts with the assumption that the properties of a compound are a function of the structural properties of the molecule and uses various molecular descriptors that reflect different structural properties. The number of molecular descriptors proposed to date has been thousands, and many kinds of molecular descriptors range from simple ones such as the number of carbons or hydrogens in a molecule to complex ones such as the shape, connection state, and electrochemical properties of molecules. Calculations have been developed for Todeschini R., V. Consonni V., Molecular Descriptors for Chemoinformatics : Second , Revised and Enlarged Edition : Volume I / II , Wiley-VCH, 2009]. The QSPR prediction model is presented in the form of a function that includes some of these molecular descriptors and sometimes, in addition, some of the other physicochemical properties of the compound, which are also functions of structural properties.

들의 선형 결합 함수이며 각 계수

들은 주로 다중선형회귀분석을 통해 실험데이터로부터 결정된다.The most frequently adopted form of such a function is

Linear coupling function of each coefficient

These are mainly determined from experimental data through multiple linear regression analysis.

이 부여되어 있다. 은닉층과 출력층의 각 노드들은 전단계의 노드들로부터 이러한 연결들을 통해 입력을 받은 뒤 이를 가공하여 출력값을 만드는데 이때 활성화 함수(activation function)라 불리는 함수

를 적용한다. 이러한 인공신경망을 실제로 활용하려면 먼저, 다양한 입력값과 그 입력값에 대응하는 출력값을 함께 묶어 놓은 샘플집합을 이용하여 인공신경망을 훈련시키는 과정이 필요한데 이는 주어진 입력에 대한 인공신경망의 출력과 원하는 출력의 차이가 최소가 되도록 역전파(back propagation) 알고리즘을 사용하여 각 연결의 가중치를 최적화 하는 것을 말한다. 이러한 훈련을 거친 인공신경망은 문제해결에 필요한 규칙이나 지식을 따로 제공하지 않아도 학습을 통해서 스스로 일반적인 규칙을 수립하여 미지의 입력에 대해서도 타당성 있는 출력을 내주므로 화합물의 물성예측과 같이 기반 이론이 결여되어 있는 분야에 매우 유용한 수단으로 널리 이용되고 있다.Another way to create a QSPR model is to use an artificial neural network. Artificial neural network technology is one of the long-standing research results of human beings who want to make intelligent machines by modeling human nerve cells with intelligence, and is an information processing technology that has been applied in various fields since the mid 20th century. . 2 shows a typical example of an artificial neural network. As can be seen, the artificial neural network has an input layer for receiving input data, an output layer for producing output data, and a hidden layer located between them, each layer having one or more nodes. ) Each node in the hidden layer is connected to nodes in the input and output layers, and each connection has a quantity called a weight.

Is granted. Each node in the hidden and output layers receives inputs from these nodes and processes them to produce output values. This is called an activation function.

Apply. In order to actually use such an artificial neural network, first, the neural network is trained using a sample set in which various input values and output values corresponding to the input values are bundled together. This means optimizing the weight of each connection using a back propagation algorithm to minimize the difference. The neural network that has undergone such training does not provide the necessary rules or knowledge to solve the problem, but it establishes general rules through learning and gives valid output for unknown inputs. It is widely used as a very useful means in the field.

Many QSPR prediction models for water solubility are not proposed, and the proposed ones also have disadvantages in that the number of sample compounds is not large or the application target is limited to a specific class of compounds. See Chunsheng Yina, Xinhui Liu, Weimin Guo, Teng Lin, Xiaodong Wang, Liansheng Wang. Prediction and application in QSPR of aqueous solubility of sulfur - containing aromatic esters using GA - based MLR with quantum descriptors . Water Research 36 (2002) 29752982 reports a model using three molecular descriptors using data for 71 compounds.

The technical problem to be solved by the present invention is to overcome the shortcomings of the existing models mentioned above and to show more broad and more accurate prediction performance, hydrogen (H), carbon (C), nitrogen (N), oxygen (O), sulfur ( It is to build a QSPR model for the water solubility of a pure organic compound composed of less than five elements such as S) and molecules having 25 or less atoms except hydrogen.

We have achieved this goal by constructing a multiple linear regression-artificial neural network hybrid model that takes into account a wider variety of molecular presenters based on more experimental data. In particular, the neural network has the advantage of reflecting the nonlinear functional relationship between independent and dependent variables, which cannot be reflected by the multiple linear regression model, so that a model with higher predictive performance can be realized. However, the artificial neural network has a disadvantage in that its stability is lower than that of the multiple linear regression model due to its high degree of freedom in rule setting. In the present invention, when the prediction value of the artificial neural network model and the prediction value of the multiple linear regression model show a large difference, the method of adopting the prediction value of the multiple linear regression model compensates for these shortcomings. We established an excellent prediction model that takes advantage of the neural network model.

The above-mentioned limitations on the range of organic compounds to which the predictive model can be applied are mainly due to the current state of the art when some of the molecular descriptors used require quantum mechanical calculations. This is due to the fact that for the compounds beyond the stated range, problems arise in terms of accuracy and calculation time. However, even within the above limitations, since there are a great many compounds and industrially important compounds are included in a large amount, it is determined that the present invention can greatly benefit human society.

Humans today depend on a wide variety of organic compounds, including plastics, fibers, rubber, paints, fertilizers, medicines and fuels, and this trend is expected to intensify. According to the American Chemical Society (ACS), as of July 2010, the total number of compounds registered was over 54,000,000. In comparison, even if the physical property value is only one, the number of experimentally known compounds is only tens of thousands. The physical property value of compounds is essential for the better life of mankind, including the development of new materials and new drugs, the optimal design of chemical plants, the improvement of the productivity of existing facilities, the development and saving of resources, the securing of safety, and the protection of the environment. Water solubility, in particular, is a very important property for new drug development, and international regulations on the production and consumption of compounds such as REACH may require them. However, at present, the number of compounds whose experimental values are known is only a few thousand, and depending on the compounds, the work of obtaining data through experiments may be past due to toxicity, instability, and difficulty of purification. From this point of view, the present invention, which can obtain the water solubility value of a large number of compounds with only the information on the molecule without experimenting, not only saves the cost and time required for the experiment, but also makes it possible to guess the value even when the experiment is impossible. In addition to facilitating the R & D activities of the industry, it will also provide effective information to all those who need the value, such as academics and academia, to facilitate the activities.

1 is a flowchart illustrating a process of constructing a multiple linear regression-artificial neural network hybrid model for water solubility provided by the present invention.
Figure 2 is a view showing the structure of the artificial neural network used in the present invention.
3 is a parity diagram of 625 experimental data of the Kuehne model, which is a group contribution model for water solubility.
4 is a parity diagram of 783 experimental data of a multiple linear regression-artificial neural network hybrid model for water solubility.
5 is a histogram diagram of 625 experimental data of the Kuehne model.
FIG. 6 is a histogram plot of 783 experimental data of a multiple linear regression-artificial neural network hybrid model.

Figure 1 is a simplified representation of the process of building a multiple linear regression-artificial neural network hybrid model for water solubility.

The first thing to do when building the model is to collect and review the experimental data as specified in step 1. As a result of extensive research on all literatures and data that can be referred to through various papers, books, and Internet sites for the present invention, a total of 1616 water solubility data for the compounds meeting the conditions of the present invention were collected. . The collected data were examined in a variety of ways to determine whether they were truly valid values that could be used to build the model.They were not experimental values, errors in data notation, or values for the same compound. After thorough analysis on the case of unreliably distant values or the values of molecular descriptors that are difficult to prepare immediately, the data were modified or deleted to finally select data for a total of 942 compounds. . And in terms of predictive performance, it was better to classify them separately into carbon and hydrogen-only hydrocarbons and nonhydrocarbons. The model was established by classification into hydrocarbons. In the present invention, the 'organic compound' or 'compound' is composed of five elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and sulfur (S). Refers to a substance consisting of molecules with 25 or fewer atoms excluded.

The next step is to prepare the values of the molecular descriptors for these compounds. The values for various molecular descriptors totaling up to 1978 are computed in batches using a computer from files containing information on the molecules of each compound. In order to calculate the electronic structure of molecules, the Schrodinger equation is usually solved by a pure theory to solve the electron energy. However, in the case of systems with many electrons, Hartley uses an approximation method that ignores electron correlation. Hartree-Fock (HF) method [CC J. Roothan, Rev. Mod. Phys. 23, 69 (1951)]. This approximation introduces a fundamental error in the calculated results and adds a multidimensional theoretical perturbation term to the Post Hartree-Fock method [C. Moller and M. S. Plesset, Phys. Rev. 46, 618 (1934)], to obtain a more accurate solution, but require a relatively large amount of computation. In this way, it is too costly or time-consuming to calculate large molecules.

In addition, the Gaussian method that combines Hartley-Fork and Post Hartley-Fork [L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 94, 7221 (1991); L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A. Pople, J. Chem. Phys. 109, 7764 (1998) show very little error in energy prediction, but more computation is required because it performs energy calculations for several post-Hartley-Fork methods.

Density functional theory is used to find the ground state using the function of the total energy using the electron density function instead of the wave function with the multidimensional perturbation term to consider the correlation between the electrons of the molecules of many electrons. R. Seeger and JA Pople, J. Chem. Phys. 66, 3045 (1977). The advantage of the density functional theory is that the electron density only needs to be taken into account so that more accurate results can be obtained with comparable calculations to the Hartree-Fock method. The combination of exchange functions and correlation functions for calculating the exchange-correlation energy of the electrons is used to obtain more improved results without increasing the calculation amount.

The computational theories previously attempted to select an optimal quantum mechanical calculation method are the density ranges of the aforementioned Hartley-Fork method, various Post-Hartley-Fork methods, Gaussian (G2, G3) methods, and various combinations of functional functions. Function theory. Among them, one method of density functional theory, which is the best performance calculation time, was selected.

Therefore, in the present invention, the optimization of the molecular structure and the frequency calculation are performed by applying the calculation method of the specified density functional theory using a commercial quantum mechanical calculation program.

In the optimized structure, not only the above physical information but also molecular descriptors represented by various meaningful values reflecting the characteristics of the molecules can be obtained. Some molecular descriptors can express the characteristics of two-dimensional structures, while others represent the characteristics of three-dimensional structures. Divided into 24 categories, including detailed presenters in each category. After calculating the molecular descriptor values, we picked out those that were not suitable, that is, the values were the same for all sample compounds and could not be independent variables in the model. This is because it prevents irrelevant molecular expressions from being included in the prediction model, thereby increasing the reliability of the model and reducing the computation time required to find the optimal model by reducing the number of molecular expressions.

In step 4, the sample compounds are divided into two parts: the training set used to explore the predictive model, and the test set used to test the predicted performance of the determined model. Sample hydrocarbons and non-hydrocarbons were divided in a ratio of 5: 5 to 8: 2, preferably 6 to 4, respectively.

이며 이들을 다 조사하는 것은 현실적으로 불가능하다.We then find the best multiple linear regression model based on the training set. The term 'best' is used in the sense of relative meaning that it can be obtained in a relatively short time and has a performance very close to the optimal solution in the absolute sense. The reason for not finding the optimal solution directly is because of the long computation time. For example, when there are 1700 suitable molecular representations out of 1978 molecular representations, you can choose from five different linear regression models. The total number is

It is practically impossible to investigate them all.

In order to obtain useful results within a limited time, the present invention provides a genetic algorithm [Judson, "Genetic Algorithms and Their Uses in Chemistry", Reviews in Computational Chemistry, Lipkowitz & Boyd, Eds., Vol. 10, pp. 1 -73 (VCH Publishers, NY, 1997)]. First, a population of multiple linear regression models is created by randomly drawing a certain number of molecular descriptors from a pool of molecular descriptors. For example, let's say we created a population of 1000 different polylinear regression models that were randomly drawn from 5 of the 1700 suitable molecular descriptors.

Individuals, called chromosomes, are coded by combining the numbers of extracted molecular descriptors. For example, the chromosome of the multiple linear regression model formed by the 45th, 167, 684, 1033, and 1502th molecular descriptors among 1700 molecular descriptors can be expressed as (45, 167, 684, 1033, 1502). Two parent chromosomes are selected from the populations thus generated and crossovered to generate children. In the present invention, the Roulette Wheel method is adopted as a selection method for selecting the parent chromosomes.

) 또는 평균절대오차(average absolute error: AAE)를 활용하였다. 즉 결정계수값이 크거나 평균절대오차값이 작은 것이 선택확률이 높도록 하였다.The Roulette Wheel method is the most commonly used selection algorithm, which allocates a roulette region to the chromosome in proportion to the fitness of each chromosome, and then rotates the roulette to select the chromosome of the corresponding region. Therefore, in this method, the higher the fit, the more likely it is to be selected. The coefficient of determination of the regression model is used to calculate the goodness of fit for each chromosome that determines the probability of selection.

) Or average absolute error (AAE). In other words, the larger the coefficient of determination or the smaller the mean absolute error, the higher the probability of selection.

The single point crossover method is adopted as the breeding method. The most common breeding method is to generate a child by selecting one crossing point on the parent chromosome and exchanging chromosomal parts before and after the point. For example, if a parent chromosome is given as (24, 262, 343, 789, 1290), (38, 454, 554, 1322, 1449) and a cross point is placed between the third and fourth elements, then the child chromosomes are (24, 262, 343, 1322, 1449), (38, 454, 554, 789, 1290).

When the offspring are created, they have a chance of mutating a portion of their chromosomes, which randomly replaces several elements with completely new values. This new information does not exist in the current population. It is a process that makes it possible to search to compensate for the case where there is no proper solution in the initial set combination.

In this way, a new generation of populations are created by replacing some or all of the existing populations with newly obtained entities. Repeat this process until the number of generations reaches a pre-determined value (usually between 10 and 1000), and then select and end up the regression model with the best predictive performance.

Once this best multiple linear regression model has been selected, the next step is to examine its validity. If a problem is found that the t-test value of the molecular descriptors included in the model is not good, go back and look for another model. For example, if the number of sample compounds is 1005 and the selected model consists of five molecular descriptors, if the t-test for one of the molecular descriptors is 3.3 or higher, then the probability that the molecular descriptor is irrelevant to that property is 0.1 It means less than%. In the present invention, when there is a molecular presenter having a t-test value of less than about 3, the selected model is discarded and another model is found. In addition, even if the values of the molecular descriptors for the sample compounds are the same except for a few few compounds, they are not considered to be reliable models. In general, increasing the number of molecular expressions included in the model increases the predictive performance, but such problems occur. Therefore, the final model is usually obtained by repeating these steps through several trials and errors while changing the number of molecular expressions. If the problem no longer appears in the selected model, proceed to the next step.

Next, in Step 7, assess the predictive performance of the found model using test sets that did not participate in model formation. If a problem is found in the training set that results in much lower predictive performance or samples that are significantly off predicted, go to step 4 and readjust the training and test sets before proceeding. If the difference between the training set and the test set does not exceed 20% of the absolute mean error (AAE) obtained for the training set, it is judged that the predictive performance is satisfied.

In this way, once the multiple linear regression model for water solubility is established, the standardization of the data of molecular presenters and the experimental data of the water solubility is first performed in order to establish the artificial neural network model. Proceed to divide by deviation. The entire sample thus prepared is divided into a training set, a validation set, and a test set in an approximately 6: 2: 2 ratio.

을, 출력층의 활성화 함수로는 선형함수 즉

를 채택하였다. 따라서 입력층의 각 노드들이 받는 입력값들을

라할 때 은닉층의 j번째 노드의 출력값은

와 같이 주어지며 은닉층이

개의 노드로 이루어져 있을 때 출력층 출력노드의 최종 출력값은

와 같이 주어진다. 여기서

는 문턱 가중치(threshold weight)를 의미한다.We then use them to find the best artificial neural network model. In this case, the search range is limited to a neural network having a hidden layer between the input layer and the output layer as shown in FIG. 2 and having three structures connected only in a feed forward direction, that is, in a direction from the input to the output. It was. The input layer is composed of the same number of nodes that receive the values of the molecular descriptors included in the already established multiple linear regression model, and the output layer is composed of one node that outputs the critical volume. In addition, as the activation function of the hidden layer, the Sigmoid function,

, The activation function of the output layer is a linear function

Was adopted. Therefore, the input values that each node in the input layer receives

Is the output value of the jth node of the hidden layer

Is given by

The final output value of the output layer output node when composed of four nodes

Is given by here

Denotes a threshold weight.

들의 다양한 초기값세트(보통1000세트이내)를 마련하고, 훈련집합을 사용하여 각 세트로 초기화된 신경망을 역전파 알고리즘을 통해 반복 훈련함으로써 가중치

들의 최적화된 값을 찾는다. 최적화에 대한 판단은 매 훈련 후 경신된 가중치들의 값으로 정해지는 모형을 검증집합에 적용하였을 때 그 평균제곱오차(mean square error)의 값이 최소가 되는 것으로 한다. 보통은 3000~5000번의 반복훈련 내에 이러한 시점이 나오게 된다. 이렇게 얻어진 각 초기값세트에 대응하는 최적화된 신경망모형을 훈련집합, 검증집합, 시험집합에 각각 적용하여 그 평균제곱오차들이 모두 다중선형회귀모형의 그것들보다 작은 것만을 모은다. 이러한 것이 여러 개 있을 경우, 결정계수나 평균절대오차 등을 기준으로 가장 우수한 모형을 선택한다.The search proceeds from increasing the number of hidden nodes to one in order. Usually, the search proceeds to twice the number of input nodes. However, if a satisfactory model is not found, the search proceeds further. The detailed procedure is as follows. First, the weight generated by using random number generation function for each number of hidden nodes

Prepare different sets of initial values (usually within 1000 sets), and then use the training set to repeatedly train the neural networks initialized in each set using a backpropagation algorithm.

Find the optimal value for these. The judgment of the optimization is that the mean square error is minimized when the model, which is determined by the updated weights after each training, is applied to the test set. Normally this will occur within 3000 to 5000 repetitions. The optimized neural network model corresponding to each set of initial values thus obtained is applied to the training set, the test set, and the test set, respectively, to collect only those whose mean square errors are smaller than those of the multiple linear regression model. If there are several of these, choose the best model based on the coefficient of determination or the absolute absolute error.

, 비탄화수소의 경우 2.5

)을 정하여 인공신경망모형과 다중선형회귀모형의 예측값들 차이의 절대값이 기준값을 넘을 경우 다중선형회귀모형의 예측값을 채택하고 이보다 작을 경우 인공신경망모형의 값을 채택하게 하는 것을 말한다.When the artificial neural network model is selected, an overfitting prevention standard is finally set. This is a measure to improve the instability that the artificial neural network gives wrong answers to unknown inputs as a result of overtraining, a reference value (0.5 for hydrocarbons).

2.5 for non-hydrocarbons

), Which means that if the absolute value of the difference between the predicted values of the artificial neural network model and the multiple linear regression model exceeds the reference value, the predicted value of the multiple linear regression model is adopted.

Through this process, the results of establishing the multiple linear regression-artificial neural network hybrid model for water solubility are shown in Table 2 (the main contents of the QSPR prediction model for the water solubility of hydrocarbon) and Table 3 (QSPR prediction for the non-hydrocarbon solubility). The main contents of the model).

Number of sample compounds 209 Number of molecular descriptors 6 Names of Molecular Presenters P ₁ : Polarizability
P ₂ : information content index (neighborhood symmetry of 0-order)
P ₃ : Radial Distribution Function-15.5 / weighted by atomic van der Waals volumes
P ₄ : Radial Distribution Function-10.0 / weighted by atomic masses
P ₅ : 3D molecular structure representation based on electron diffraction-order 30 / weighted (3D-MoRSE-signal 30 / unweighted)
P6: shape profile no.13 Regression Model Decision Coefficients 0.961322 Regression Model Mean Absolute Error

0.276024

Regression model Water solubility [ ] =

Artificial Neural Network Determination Coefficient 0.966531 Artificial neural network mean absolute error 0.261894

Artificial Neural Network Model Acceptance =

Overconformity Prevention Criteria 0.5

Number of sample compounds 733 Number of molecular descriptors 10 Names of Molecular Presenters P ₁ : Octanol-Water partition coefficient
P ₂ : Polarizability
P ₃ : sp3 carbon / sp2 carbon / sp2 carbon / sp carbon bonded hydrogen (H attached to C3 (sp3) / C2 (sp2) / C3 (sp2) / C3 (sp))
P ₄ : Radial Distribution Function-14.0 / weighted by atomic masses
P ₅ : Maximum net atomic charge for a H atom
P ₆ : Radial Distribution Function-6.0 / weighted by atomic Sanderson electronegativity
P ₇ : HDSA H-donors surface area
P ₈ : Minimum electrophilic reactivity index for a O atom
P ₉ : Radial Distribution Function-4.0 / unweighted
P10: Moran autocorrelation-lag 2 / Weighted by atomic masses Regression Model Decision Coefficients 0.846716 Regression Model Mean Absolute Error

0.483452

Regression model Water solubility [

] =

Artificial Neural Network Determination Coefficient 0.904979 Artificial neural network mean absolute error 0.377491

Artificial Neural Network Model Acceptance =

Overconformity Prevention Criteria 2.5

의 평균절대오차값을 가짐을 알게 되었다. 반면 다중선형회귀-인공신경망 혼성모형은 783개 전부에 대해 예측값을 계산해주며 0.983585의 결정계수값과 0.23135

의 평균절대오차값을 가져 기존 모형보다 우수함을 알게 되었다. 도 2, 3는 각 모형의 예측성능을 보여주는 패리티(parity) 도면들이며 이 도면들로부터 다중선형회귀-인공신경망 혼성모형이 기존 모형보다 우수한 성능을 가짐을 눈으로 확인할 수 있다. 한편 수용해도값의 실험평균오차는 약 0.45

이며 이 값을 중심으로 실험값과 예측값 사이의 오차를 히스토그램으로 그린 것이 도 4, 5이다. 이 도면들은 KUEHNE 모형은 33.28%, 다중선형회귀-인공신경망 혼성모형은 90.55%의 확률로 평균 실험오차의 범위 이내로 수용해도값을 예측하고 있음을 보여주어 다중선형회귀-인공신경망 혼성모형이 기존 모형보다 정확함을 증명해준다.
In order to show that the present invention is superior to the existing technology, the multilinear regression-artificial neural network hybrid model thus established and the existing group contribution model widely used, that is, Kuehne model [Kuene R., Ebert RU, Kleint F., Schmidt G., Group Contribution Methods to Estimate Water Solubility of Organic Chemicals , Chemosphere, 1995.30.2061] were compared using data from 783 compounds with known experimental values. As a result, the KUEHNE model calculates the predicted value for only 625, and the coefficient of determination of 0.612319 and 1.05504

It is found that the mean absolute error of. On the other hand, the multiple linear regression-artificial neural network hybrid model calculates the predicted values for all 783, and has a coefficient of determination of 0.983585 and 0.23135.

The average absolute error of was found to be superior to the existing model. 2 and 3 are parity diagrams showing the predictive performance of each model, and it can be seen from these figures that the multilinear regression-artificial neural network hybrid model has better performance than the conventional model. On the other hand, the experimental mean error of water solubility value is about 0.45

Figures 4 and 5 show the histogram of the error between the experimental value and the predicted value. These figures show that the KUEHNE model predicts acceptability values within 33.28% of the KUEHNE model and 90.55% of the multiple linear regression-artificial neural network hybrid models. It proves more accurate.

The present invention is not limited to the above-described embodiments, and any person having ordinary skill in the art to which the present invention pertains may make various modifications without departing from the gist of the present invention as claimed in the claims. Such changes are intended to fall within the scope of the claims.

Claims (28)

A first step of inputting hydrocarbon-based experimental data among collected sample organic compounds;
A second step of preparing a molecular presenter value for the water solubility of the hydrocarbon-based organic compound input in the first step;
Extracting optimal molecular descriptors;
A fourth step of separating the experimental data into a training set and a test set;
A fifth step of searching for an optimal multiple linear regression model for the training set;
A sixth step of examining the validity of the selected model;
A seventh step of repeating the fifth and sixth steps if there is no validity in the sixth step, and testing the predictive performance of the model with respect to the test set if it is valid;
An eighth step of repeating steps 4 to 7 if the performance does not satisfy the criterion in the seventh step test for the test set, and separating the three sets after sample normalization if the criterion is satisfied;
A ninth step of searching for an optimal neural network model after dividing the entire sample into three sets;
Preventing overfitting the absolute value of the water solubility prediction value obtained by the optimal linear regression model satisfying the performance test in the eighth step and the absolute value difference between the water solubility prediction values obtained by the optimal neural network model found in the ninth step A tenth step of comparing with a reference value; And
If the difference is greater than the overfit reference value, the water solubility prediction value obtained by the multiple linear regression model obtained in the eighth step is taken as the acceptability value, and if the difference is less than the overfit reference value, the artificial neural network model discovered in step 9 A water solubility of a hydrocarbon-based organic compound is obtained through a multiple linear regression-artificial neural network model comprising the eleventh step of adopting a water solubility prediction value as a water solubility value.
The method of claim 1, wherein in the third step, the optimal molecular descriptor is an independent molecular descriptor whose values are not the same for all the sample compounds, and the hydrocarbon-based organic compound is accepted through the multiple linear regression-neural network model. How to get a chart.
The method of claim 1, wherein the training set and the test set are divided by a ratio of 5: 5 to 8: 2 in the fourth step. .
2. The multiple linear regression-artificial neural network model according to claim 1, wherein in the fifth step, the multiple linear regression model searches for a multiple linear regression model by applying a genetic algorithm to the training set. Method for obtaining the water solubility of a hydrocarbon-based organic compound through.
The method of claim 4, wherein the genetic algorithm generates a population composed of a plurality of multiple linear regression models randomly drawn from a predetermined number of molecular representations in a pool of molecular representations. Making; Encoding each individual by combining the numbers of the extracted molecular presenters; Selecting two parent chromosomes from the created population by the Roulette Wheel method and generating offspring by a single point crossover method; Hydrocarbon-based organics through a multiple linear regression-artificial neural network model comprising the step of mutating a portion of the chromosome of the generated offspring with a certain probability and then replacing a part of the existing population with them to create a new population. A method of determining the water solubility of a compound.
The method of claim 1, wherein the fifth step includes determining the predictive performance based on a coefficient of determination or an average absolute error of the regression model through a multiple linear regression-artificial neural network model.
The method of claim 1, wherein the validity in the sixth step is to determine the water solubility of the hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model in which the validity is determined by a t-test value.
The method of claim 1, wherein in the eighth step, if the predictive performance of the test set is similar to the predicted performance of the training set, a multiple linear regression model is determined, and the predictive performance of the test set is different from the predicted performance of the training set. The standard water solubility of a hydrocarbon-based organic compound is then obtained through a multiple linear regression-artificial neural network model that reclassifies the training set and the test set.
The method of claim 1, wherein in the ninth step, the search range by the neural network has one hidden layer between the input layer and the output layer and is connected only in a feed forward. Method of obtaining water solubility of hydrocarbon-based organic compounds by neural network model.
10. The method of claim 9, wherein a sigmoid function is used as the activation function of the hidden layer.
The method of claim 1, wherein the reference value for preventing overfitting is 0.5 in the tenth step. The water solubility of the hydrocarbon-based organic compound is obtained through a multiple linear regression-artificial neural network model.
A first step of inputting non-hydrocarbon-based experimental data among collected sample organic compounds;
A second step of preparing molecular expression values for water solubility of the hydrocarbon-based organic compounds of sample organic compounds;
Extracting optimal molecular descriptors;
A fourth step of separating the experimental data into a training set and a test set;
A fifth step of searching for an optimal multiple linear regression model for the training set;
A sixth step of examining the validity of the selected model;
A seventh step of repeating the fifth and sixth steps if there is no validity in the sixth step, and testing the predictive performance of the model with respect to the test set if it is valid;
An eighth step of repeating the fourth to seventh steps if the performance is not satisfied in the seventh step test on the test set, and separating the three sets after normalizing the sample if the performance is satisfied;
A ninth step of searching for an optimal neural network model after dividing the entire sample into three sets;
Preventing overfitting the absolute value of the water solubility prediction value obtained by the optimal linear regression model satisfying the performance test in the eighth step and the absolute value difference between the water solubility prediction values obtained by the optimal neural network model found in the ninth step A tenth step of comparing with a reference value; And
If the difference is greater than the overfit reference value, the water solubility prediction value obtained by the multiple linear regression model obtained in the eighth step is taken as the acceptability value, and if the difference is less than the overfit reference value, the artificial neural network model discovered in step 9 The water solubility of the non-hydrocarbon-based organic compound is obtained through the multiple linear regression-artificial neural network model including the eleventh step of adopting the water solubility prediction value as the water solubility value.
13. The method of claim 12, wherein the optimal molecular descriptors in the third step are independent molecular descriptors whose values are not the same for all the sample compounds. How to get water solubility.
The method of claim 12, wherein the training set and the test set in the fourth step to obtain the water solubility of the non-hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model, characterized in that divided by the ratio of 5: 5 ~ 6: 4 Way.
13. The method of claim 12, wherein in the fifth step, the multiple linear regression model searches for the multiple linear regression model by applying a genetic algorithm to the training set. Method for obtaining the water solubility of non-hydrocarbon organic compounds through.
The method of claim 15, wherein the genetic algorithm generates a population composed of a plurality of multiple linear regression models randomly drawn from the pool of molecular presenters. Making; Encoding each individual by combining the numbers of the extracted molecular presenters; Selecting two parent chromosomes from the created population by the Roulette Wheel method and generating offspring by a single point crossover method; A non-hydrocarbon series through a multiple linear regression-artificial neural network model comprising the step of mutating a portion of the chromosomes of the generated offspring with a certain probability and then replacing a portion of the existing population with them to create a new population. Method for obtaining the water solubility of organic compounds.
The method of claim 12, wherein the fifth step is to determine the water solubility of the non-hydrocarbon-based organic compound through the multiple linear regression-artificial neural network model including determining the predictive performance by the regression model crystal coefficient or the mean absolute error. .
The method of claim 12, wherein the validity in the sixth step is to determine the water solubility of the non-hydrocarbon-based organic compound through the multiple linear regression-artificial neural network model that determines the validity by the t-test value.
The method of claim 12, wherein in the eighth step, if the predictive performance of the test set is similar to the predicted performance of the training set, a multiple linear regression model is determined, and the predictive performance of the test set is different from the predicted performance of the training set. The standard water solubility of the non-hydrocarbon-based organic compounds is then obtained through a multiple linear regression-artificial neural network model that reclassifies the training set and the test set.
The method of claim 12, wherein in the ninth step, the search range by the artificial neural network has one hidden layer between the input layer and the output layer and is connected only in a feed forward. A method of obtaining water solubility of non-hydrocarbon organic compounds by neural network model.
21. The method of claim 20, wherein a sigmoid function is used as the activation function of the hidden layer.
The method of claim 12, wherein in the tenth step, the reference value for preventing overfitting is 2.5, wherein the water solubility of the non-hydrocarbon-based organic compound is obtained through a multiple linear regression-artificial neural network model.
The method of claim 1, wherein the optimal molecular descriptors extracted in the third step
P ₁ : Polarizability,
P ₂ : information content index (neighborhood symmetry of 0-order),
P ₃ : Radial Distribution Function-15.5 / weighted by atomic van der Waals volumes,
P ₄ : Radial Distribution Function-10.0 / weighted by atomic masses,
P ₅ : 3D molecular structure representation based on electron diffraction-order 30 / unweighted (3D-MoRSE-signal 30 / unweighted) and
P ₆ : shape profile no. 13
A method for obtaining the water solubility of a hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model.
The method of claim 12, wherein the optimal molecular descriptors extracted in the third step is
P ₁ : Octanol-Water partition coefficient,
P ₂ : polarization (Polarizability),
P ₃ : sp3 carbon / sp2 carbon / sp2 carbon / sp carbon bonded hydrogen (H attached to C3 (sp3) / C2 (sp2) / C3 (sp2) / C3 (sp)),
P ₄ : Radial Distribution Function-14.0 / weighted by atomic masses,
P ₅ : Maximum net atomic charge for a H atom
P ₆ : Radial Distribution Function-6.0 / weighted by atomic Sanderson electronegativity,
P ₇ : HDSA H-donors surface area,
P ₈ : Minimum electrophilic reactivity index for a O atom,
P ₉ : Radial Distribution Function-4.0 / unweighted and
P ₁₀ : Moran autocorrelation-lag 2 / Weighted by atomic masses
Method for obtaining the water solubility of the non-hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model.
In the method for determining the water solubility of hydrocarbon-based organic compounds through multiple linear regression-artificial neural network model,
P ₁ : Polarizability
P ₂ : information content index (neighborhood symmetry of 0-order),
P ₃ : Radial Distribution Function-15.5 / weighted by atomic van der Waals volumes,
P ₄ : Radial Distribution Function-10.0 / weighted by atomic masses,
P ₅ : 3D molecular structure representation based on electron diffraction-order 30 / unweighted (3D-MoRSE-signal 30 / unweighted) and
P ₆ : shape profile no. 13
Method for obtaining the water solubility of a hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model comprising a.
In the method for determining the water solubility of non-hydrocarbon type organic compounds by multiple linear regression-artificial neural network model,
P ₁ : Octanol-Water partition coefficient,
P ₂ : polarization (Polarizability),
P ₃ : sp3 carbon / sp2 carbon / sp2 carbon / sp carbon bonded hydrogen (H attached to C3 (sp3) / C2 (sp2) / C3 (sp2) / C3 (sp)),
P ₄ : Radial Distribution Function-14.0 / weighted by atomic masses,
P ₅ : Maximum net atomic charge for a H atom,
P ₆ : Radial Distribution Function-6.0 / weighted by atomic Sanderson electronegativity,
P ₇ : HDSA H-donors surface area,
P ₈ : Minimum electrophilic reactivity index for a O atom,
P ₉ : Radial Distribution Function-4.0 / unweighted and
P ₁₀ : Moran autocorrelation-lag 2 / Weighted by atomic masses
Method for obtaining the water solubility of the non-hydrocarbon-based organic compound through a multiple linear regression-artificial neural network model, characterized in that it comprises a.
A computer-readable recording medium having a computer program for executing the method for obtaining the water solubility of a hydrocarbon-based organic compound according to any one of claims 1 to 11, 23 and 25.
A computer-readable storage medium having recorded thereon a program for executing on a computer a method for obtaining the water solubility of the non-hydrocarbon-based organic compound according to any one of claims 12 to 22, 24 and 26.

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