# Polynomial Neural Network Discovery Client User Guide

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1 Polynomial Neural Network Discovery Client User Guide Version 1.3

2 Table of contents Table of contents Introduction Overview PNN algorithm principles Additional criteria PNN algorithm features PNN data format General information General information System requirements Package contents Installation and software activation How to get PNN Discovery Client Technical support Using PNN Discovery Client Getting started Project-oriented approach Opening project Creating new project Saving project PNN framework toolbar and menu Toolbar buttons Additional menu items Panels Table View HTML View Chart View Plot View Project options Calculations Import and export Text Import Wizard Microsoft Excel Import Wizard Export Wizard

3 1. Introduction 1.1 Overview PNN is self-organizing multi-layered iterative Polynomial Neural Network algorithm. It is one of the most promising solutions from GMDH-type neural network algorithms family. PNN supports both linear and non-linear polynomial regression models. Polynomial Neural Network (PNN) algorithm can be used to analyze complex data sets, find out internal data relationships and present knowledge about these relationships in the form of mathematical description (polynomial regression equation). Application area of PNN algorithm may include any domain where sets of observation data should be analyzed and data relationship models should be built. Chemistry (QSAR), economical systems analysis, stocks and financial market instruments, insurance risks study and medical diagnostics can be considered as good examples. 1.2 PNN algorithm principles To be processed with PNN algorithm, the data have to be organized in a specific way. Let us give definitions for terms used throughout this guide. A set of observed quantitative parameters {x 1, x 2,..., x m } forms the vector of input variables x. Each observation x (input) has an "already known" result y (output). The purpose of the algorithm is to find a subset of variables {x i1, x i2,..., x ik } and a model y = f i (x i1, x i2,..., x ik ) in the set of polynomials of s-power that minimizes some criterion value (CR). After the model is built, you can use it for prediction of yet unknown result y that corresponds to newly observed vector X. The algorithm is implemented as a GMDH-type Neural Network. First layer generates the models y = g(x i, x j, x k ), where x i, x j, x k are input variables. Next layers generate models as y = g(w i, w j,w k ), where w i, w j,w k are the models of previous layers that minimize criterion value (CR). See figure below. 1.3 Additional criteria 2 n m Least-squares estimation criterion min y i β j f ji β 1,...β m is the best for models with normal distribution i=1 j=1 of errors. Still it is well known that this criterion is sensitive to outliers in the data set. In case outliers are n m min β 1,...β m ρ ( y i β j f ji ) present, Robust PNN uses modified least-squares estimation criterion: i=1 j =1. Instead of raising to the second power, function ρ() is used: ρ (z) = (1/2)z2 Cz- (1/2)C 2 The standard criteria of model estimation are: if z C if z > C. 3

4 Rest Minimal Square Errors RMSE = Coefficient of correlation r 2 = Cross validated criterion q 2 =1 1 ( y pred y actual ) 2 n ( y pred y pred )y actual y actual ( ) ( y pred y pred ) 2 y actual y actual 1 n 1 n ( y pred y actual ) 2 ( y actual y mean ) 2 ( ) 2 These criteria are based on minimal squares and sensitive to outliers as well as MSE method itself. Therefore, in case outliers are present, Robust PNN uses modifications of standard RMSE and q 2 criteria to characterize models more adequately. The modified criteria use the same ρ() function as least-squares criterion. RMSE = q 2 =1 1 n 1 n 1 n ρ( y pred y actual ) ρ( y pred y actual ) ρ( y actual y mean ) 1.4 PNN algorithm features The main features of the algorithm can be summarized as follows: Fast learning. The transforms with two coefficients only are used, for example g(w i, w j ) = a w i +b w j in the linear case. Irrespectively of the power of resulting model and the number of terms the second order matrices are only inverted. The latter enables fast learning of the algorithm. Results in the parametric form. The polynomial structures are coded using vector of simple numbers that provides the presentation of the results in the parametric form of nonlinear equation. Complexity control against overfitting of model. Contrary to traditional GMDH algorithm, using of Gedel numbers for model structure coding allows us to control the complexity of each intermediate model during selection. We consider as complexity the vector (power, c) T, where power is the power of the polynomial and c is the number of terms. It gives us the possibility to restrict the class of the models under consideration by power(w i ) < p and to search models among the polynomials with power less than p. The maximum complexity is defined by the user or can be automatically selected using a full cross-validation method. Twice-hierarchical neural net structure. Twice-hierarchical neural net structure is important feature of PNN. One of the problems of traditional GMDH algorithms is that power of polynomials increases too fast. The control of complexity gives us an opportunity to implement the iteration procedure without an increase of the power of polynomials or/and the number of terms. Twice-hierarchical neural net includes Internal and External nets. Internal iterative procedure provides a wide search under the fixed complexity. External procedure controls the complexity, i.e. the number of the terms and the power of the polynomials. Moreover, the twice-hierarchical neural net structure provides the convergence of the coefficients. The models, which are calculated as a result of several transformations, have the coefficients that are close to the appropriate regression coefficients. 4

5 Robust estimation. To use algorithm in the presence of large errors (outliers) we have developed the PNN algorithm for robust nonlinear (M-regression) model identification (RPNN). It allowed us to improve stability of PNN algorithm. More details about PNN algorithm you can find here PNN data format PNN algorithm deals with matrix dataset. Dataset is formally divided into three parts. First set of rows is involved in learning of PNN algorithm and searching best models. These rows are named training rows. Second set of rows could be involved in models estimation and ranking only. We call these rows test subset. And third set of rows could be involved in building approximation values of output values using result models. We call these rows validation subset. 5

7 3. Using PNN Discovery Client 3.1 Getting started PNN Discovery Client is a full-fledged standalone application running under Windows operation system. PNN Discovery Client allows users to prepare spreadsheet data, find out the best regression models and view obtained results as tabular data or special chart presentations. PNN Discovery Client offers a range of tools to export data and results in Microsoft Excel workbook, text, HTML and XML format. The PNN Discovery Client layout consists of two panels (see figure 3.1 below): Data view panel Results view panel Figure 3.1 Each panel allows selecting a view best suited for one s needs. Figure 3.1 shows default appearance of panels: Table View in Data panel and HTML View in Results panel. Toolbar buttons provide quick access to general commands and functions (see figure 3.2). 7

8 Figure Project-oriented approach PNN Discovery Client has project-oriented design for managing separate analyses (projects) in multithreading environment under a single PNN framework. PNN project contains original data, results of analysis and configuration settings. When saved on disk, the PNN project file by default has the extension.pnn Opening project Click on button in the toolbar or select File -> Open menu command to open previously saved project file. Alternatively, double click on the file in Windows Explorer. Most recent projects can be accessed from the File -> Recent Files submenu Creating new project Click on button in the toolbar or select File -> New menu command to open new project. New project will be opened in the separate window Saving project Click on button in the toolbar or select File -> Save menu command to save project file. Standard Windows Save File dialog appears. 3.3 PNN framework toolbar and menu Toolbar buttons 8

9 New Project create new project in separate window Open Project file open previously saved project file Save Project save current project data, settings and results in the.pnn file Show/hide resulting panel show or hide resulting panel in the framework. Search models start PNN algorithm calculations Stop break algorithm execution Pause suspend/proceed algorithm execution Settings set PNN algorithm parameters Apply models input dataset substitution to resulting models and calculating approximation values Additional menu items Some functionality is available only through PNN framework menu: Options general settings for PNN Discovery Client framework Split Vertically you can choose to split main framework vertically or horizontally Import External Data invokes Wizard to import data from plain text files, XML files and Microsoft Excel workbooks Export To invokes Wizard to export data and/or results to one of the following formats: tab delimited plain text (*.txt), comma delimited plain text (*.csv), XML (.xml) and Microsoft Excel workbook (.xls) 3.4 Panels Every panel has its own toolbar that allows you to select and customize the view. On the Data panel you can add, remove and edit rows and columns of the spreadsheet. Current version supports the only view for Data panel: Table View Results panel provides an access to results presentation in different ways. The following views are available for Results panel: HTML View Chart View Plot View Data panel is always open in the PNN framework and cannot be closed. Data panel can be hidden. Results panel can be closed or hidden anytime Table View Table View displays data sheet that allows user add/delete/modify rows and columns. Redo/Undo functionality is also available. (See figure 3.5.1). 9

10 Figure Columns of the data sheet represent independent variables and rows are observations of these variables. Last column of the data sheet is named target column and contains observable function value. The data sheet should have at least 3 rows and 3 columns (not including target column). Default size of Table View data sheet is 3x3. The button in the control toolbar allows you to set custom initial size of the data sheet (see figure below). The button in the control toolbar clears all data and restores initial size of the data sheet. Table View Toolbar Table below describes Table View toolbar functionality: Custom grid. Set custom initial size of the data sheet Clear / Reset table. Clear all data and restore initial size of the data sheet Add row. Add new row at the end of the data sheet Insert row. Insert row before current selection in the data sheet. Some cell or rows must be selected in the data sheet Delete row. Delete selected row(s). Some cell or rows must be selected in the data sheet Add column. Add new column as last variable column Insert column. Insert column before current selection in the data sheet. Some cell or columns must be selected in the data sheet Delete column. Delete selected column(s). Some cell or columns must be selected in the data sheet Swap column with Target. Swap selected column with target column Undo last changes Redo last changes 10

11 Table View Properties Click on button in the control toolbar to invoke Table View Properties dialog. Or you can invoke it from the Table View context menu. Table View Properties dialog is shown below. General tab: Initial rows size initial number of rows in the data sheet Initial columns size initial number of columns in the data sheet Initial cells value initial cell value in the data sheet View grid headers grid headers style (flat or raised headers) Decimal digits number of decimal digits after decimal point Apply to all projects apply current settings for new projects Default reset all values to default state Colors tab: Learning subset cells background color for cells that used for algorithm learning Alternate learning subset cells alternate background color for cells that used for algorithm learning Test Learning subset cells background color for cells that used only for testing 11

12 Alternate Test subset cells alternate background color for cells that used only for testing HTML View HTML View displays formatting report with results of PNN algorithm calculations (See figure 3.5.2). Figure The report includes the following sections showing the result of best models searching: Settings list of algorithm settings Input data sheet data sheet records Resulting equations list of resulting regressions and criteria values for regressions and test subset (Main criteria criteria values for models; Testing criteria criteria calculated based on test subset) Approximation comparison with target values 12

13 Additional external criteria additional criteria to estimate quality of obtained regressions Also, the report includes two additional sections represented the model s applicability to the input dataset: Resulting approximation input dataset substitution to the resulting equations Input dataset input dataset records Report in HTML View can be generated in 2 formats: as HTML and as plain text. The button in the HTML View control toolbar allows you to save report in.html file. Click on button in the HTML View control toolbar to print current report. HTML View Toolbar Clear content. Clear all resulting report in HTML View. To view the same resulting report again reload HTML View control in the control combo box in Results panel Refresh. Refresh reporting layout Save As HTML file. Save resulting report in the HTML file in the file system Print. Print resulting report HTML View Properties Click on button in the control toolbar to invoke HTML View Properties dialog. Or you can invoke it from the HTML View context menu. General tab: Result as switch report format between HTML and plain text Font size set font size: Large, Normal or Small Settings enable/disable Settings section in the report Input data sheet enable/disable Data sheet section in the report (disabled by default) Models and criteria values - enable/disable Models section in the report Approximations - enable/disable Approximation section in the report Estimation - enable/disable Estimation section in the report Decimal digits number of decimal digits after decimal point Apply models display models applicability to the input dataset in the report Apply to all projects apply current settings for new projects 13

14 Colors tab: Table headers background color for table headers in the report Target column background color for target column values Validation set background color for validation rows Section headers color for section headers Background background color for regular cells XSLT tab: XSLT file for HTML presentation XSLT file location to make custom HTML report presentation based on PNN Discovery Client XML standard. XSLT file for TEXT presentation XSLT file location to make custom TEXT report presentation based on PNN Discovery Client XML standard. The XSLT file templates (pnn.xslt and pnntxt.xslt) are included into the PNN Discovery Client installation Chart View Chart View shows deviation of approximation values from target values in resulting models (See figure 3.5.3). 14

15 Figure You can navigate throughout the models using buttons on the control toolbar. Chart View Toolbar First chart. Show chart for first model Previous chart. Show chart for previous model Next chart. Show chart for next model Last chart. Show chart for last model Save image. Save chart as bitmap file Chart View properties Click on button in the control toolbar to invoke Chart View Properties dialog. Or you can invoke it from Chart View context menu. 15

16 General tab: Swap axes swap Approximation and Target axes Show legend show legend for chart symbols Show all models show charts for all models Allow maximum maximum number of charts shown in the view simultaneously Show criteria show criteria value below the chart Show filter dialog when saving image on disk show dialog for custom save options Apply to all projects apply current settings for new projects Appearance tab: Chart area background color of background inside chart area Ruler background color of background around chart Ruler text color for all labels on the chart 16

17 Marks/Nodes tab: Main subset s points type, color and size of marks for main subset points Test subset s points - type, color and size of marks for test subset points Plot View Plot View allows comparison between approximation models and target shown as functions of their arguments (See figure 3.5.4). You can navigate throughout the models using buttons on the control toolbar. Figure Plot View Toolbar First chart. Show chart for first model 17

18 Previous chart. Show chart for previous model Next chart. Show chart for next model Last chart. Show chart with last model Save image. Save plot as bitmap file Plot View properties Click on button in the control toolbar to invoke Chart View Properties dialog. Or you can invoke it from Chart View context menu. General tab: Swap axes swap Approximation and Target axes Show legend show legend for plot symbols Show all models show plots for all models on a single chart Allow maximum maximum number of plots shown on a single chart Show criteria show criteria value below the plot Show filter dialog when saving image on disk show dialog for custom save options Apply to all projects apply current settings for new projects 18

19 Appearance tab: Chart area background color of background inside plot area Ruler background color of background around plot Ruler text color for all labels on the plot Marks/Nodes tab: Target node type, color and size of target points Approximation node - type, color and size of approximation points Lines tab: Target color and thickness of line that links target values Approximation color and thickness of line that links approximation values 3.5 Project options PNN Discovery Client framework menu command View -> Options allows you to customize general setting for newly created projects. 19

20 On View tab you can select Views that will be displayed in Data panel and Result panel by default. Also you can select the layout for main framework window. Check Split framework window vertically checkbox to split work area vertically. Check Show reminder window checkbox to show Save Project dialog every time you close the project. On General tab you can set default parameters for PNN algorithm. See details below in Calculations section. 20

21 On Advanced tab you can set default advanced parameters for PNN. See details below in Calculations section. On Criteria tab you can set additional external criteria to estimate quality of resulting regressions. Two criteria are available: Correlation coefficient (well-known as r2 criteria) Cross validated correlation coefficient (like SIBYL q2 estimation) On Preprocessing tab you can specify additional preprocessing operations for initial data to increase quality of resulting regressions. The following preprocessing operations are available now: 21

22 Exclude from searching process variables with specified value of correlation coefficient 3.6 Calculations To achieve better results and higher accuracy of regression models you may consider adjusting parameters of PNN algorithm. You may access current parameters of PNN algorithm by clicking button in the PNN Discovery Client framework toolbar (see figure below). 22

23 Type of regression equation type of polynomials equations that will be targeted by PNN algorithm. There are 4 types of regression supported by PNN algorithm, which cover all possible types of polynomial equations. Criteria type type of criteria used for estimation and ranking of best models. Now, 2 types of criteria are supported: RSS (excluding values in validation rows) and RR (including only values in validation rows). Maximal terms number in equations number of terms in equation defines complexity of the regression models Maximal iterations number Number of iterations used in PNN algorithm on each complexity layer Maximal number of saved models number of models that will be rotated in the course PNN algorithm calculation Maximal equations degree degree of polynomial equation Rows number in test subset Number of rows excluded from the training set (see 1.4 for more details) For robust models estimation you have to set parameters for robust calculations. Zero value for number of robust iterations disables robust models estimation. In addition, it is possible to look for regression models with specific term types: Quadratic fractional terms - terms like 2, n 0, n < 0 and values in spreadsheet must be positive n Logarithm terms - terms like log x, n 0 and values in spreadsheet must be positive Fractional terms - terms like is 1/x and values in spreadsheet must be nonzero. x n Maximal iterations number used for robust coefficient estimation internal parameter of M- estimation. Increase in number of iterations for robust estimation leads to increase in time of models searching. Fixed parameter value can take values from the interval 1.0 to 1.5 (Default value is 1.0). 23

24 To include additional external criteria estimation for resulting regressions, set criteria parameters. Two additional criteria included in the PNN Discovery Client: Correlation coefficient well known as r2 criteria Cross-validated correlation coefficient - like SIBYL q2 estimation To include additional data preprocessing and increase quality of resulting regressions, set preprocessing parameters. Now, the only data preprocessing operation, included to the PNN Discovery Client is: Exclude variables with correlation coefficient variables with given value of correlation coefficient excluded from searching process. 24

25 Click on button in the PNN Discovery Client framework toolbar to start searching the best models with PNN algorithm. Click on button to break searching best models any time processing takes place. Click on button to suspend execution temporarily, so you can resume it later by clicking again. If you change data in the spreadsheet or parameters of PNN algorithm while calculation is going on, changes will be effective next time you start calculations. Calculation progress is shown in status bar of PNN Discovery Client framework (see figure above). 3.7 Import and export The PNN Discovery Client supports import of data presented in the following formats: plain text (.txt), XML (.xml), Microsoft Excel workbooks (.xls) Text Import Wizard On the first page you can select data format: delimited values or fixed size columns. 25

26 Also, you can specify the range of rows you are going to import. For delimited data on the second page you can specify symbol(s) treated as delimiter and exclude columns you are not going to import. 26

27 For fixed data on the second page you can specify column width for each column and exclude columns you are not going to import. On each step, you can monitor and verify correctness of export settings. And on the last page you can select target column and rows that will be treated as validation set. You can select to treat first row as columns (variables) names. Click Finish button to start import of data. Imported data is displayed in the current Data panel View. For huge data sheets, import may take some time Microsoft Excel Import Wizard Microsoft Excel Import wizard allows importing data from Microsoft Excel workbook. On the first page you can select worksheet or named cell range from which data is to be imported. 27

28 On the second page you can specify columns and rows you wish to skip during import operation. On the third page you can specify target column and rows that will be treated as validation set. Also, by selecting first row as columns headers, you can define names for variables. 28

29 And on the last page you can specify conversion precision for real values (number of decimal digits after decimal point). Click Finish button to start import of data. Imported data is displayed in the current Data panel View. For huge data sheets, import may take some time. 29

30 3.7.3 Export Wizard Select menu command Tools -> Export To in the PNN Discovery Client framework menu to export input data sheet and best models found to following formats: tab delimited plain text (*.txt), comma delimited plain text (*.csv), XML (.xml) and Microsoft Excel workbook (.xls). Specify information, you wish to export - input data sheet and/or models found. Export Wizard saves it in the selected format. Note. Number of columns in Microsoft Excel spreadsheet is limited to 256 columns. Therefore, we recommend using our Export Wizard to export large data sheets to Microsoft Excel format. Our Export Wizard guarantees correctness of data layout on the Microsoft Excel spreadsheet. 30

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