*********** Iris.nns is a NeuNet Pro Sample File *********** This file contains special properties that allow NeuNet Pro to recognize it as authorized NeuNet sample data. Anyone using the unlicensed version of NeuNet Pro is welcome to experiment with this sample data. Please do not modify this file, or it will lose its status as authorized sample data. For further information about Neunet Pro and additional sample data, please visit the NeuNet Pro website at http://www.cormactech.com/neunet All of this data has been collected from publicly available sources. CorMac Technologies Inc. does not guarantee the accuracy of the data. This data is intended solely for experimental purposes. *************** More about the Iris Data ******************* ##################### # The Iris database # ##################### 1. Sources: (*) This database is taken from the ftp anonymous "UCI Repository Of Machine Learning Databases and Domain Theories" (ics.uci.edu: pub/machine-learning-databases). (a) Original source: Anderson, E. (1935) "The Irises of the Gaspe Peninsula", Bulletin of the American Iris Society, 59, 2-5. Made famous by R. A. Fisher. (b) Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov) 2. Past Usage: Publications: too many to mention!!! Here are a few. 1. Fisher,R.A. "The use of multiple measurements in taxonomic problems" Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to Mathematical Statistics" (John Wiley, NY, 1950). 2. Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis. (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218. 3. Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System Structure and Classification Rule for Recognition in Partially Exposed Environments". IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No. 1, 67-71. 4. Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule". IEEE Transactions on Information Theory, May 1972, 431-433. 5. See also: 1988 MLC Proceedings, 54-64. Cheeseman et al's AUTOCLASS II conceptual clustering system finds 3 classes in the data. 3. Relevant Information: This is perhaps the best known database to be found in the pattern recognition literature. Fisher's paper is a classic in the field and is referenced frequently to this day. (See Duda & Hart, for example.) The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant. One class is linearly separable from the other 2; the latter are NOT linearly separable from each other. Predicted attribute: class of iris plant. This is an exceedingly simple domain. 4. Attribute Information: 1. sepal length in cm 2. sepal width in cm 3. petal length in cm 4. petal width in cm 5. class: Iris Setosa: class 0 Iris Versicolour: class 1 Iris Virginica: class 2 5. Examples: 5.1 3.5 1.4 0.2 0 4.9 3.0 1.4 0.2 2 4.7 3.2 1.3 0.2 0 4.6 3.1 1.5 0.2 1 6. Summary Statistics: Attribute Min Max Mean Standard deviation 1 4.3 7.9 5.84 0.83 2 2.0 4.4 3.05 0.43 3 1.0 6.9 3.76 1.76 4 0.1 2.5 1.20 0.76 Class Distribution: number of instances per class class 0 50 - 33.3% class 1 50 - 33.3% class 2 50 - 33.3% Correlation matrix: {{ 1.00,-0.11, 0.87, 0.82}, {-0.11, 1.00,-0.42,-0.36}, { 0.87,-0.42, 1.00, 0.96}, { 0.82,-0.36, 0.96, 1.00}} Attributes maximum precision: 10 bits. The database resulting from the centering and reduction by attribute of the iris database is on the ftp server in the `REAL/iris/iris_CR.dat.Z' file. 7. Confusion matrix obtained with the k_NN classifier on the iris_CR.dat database (with the Leave_One_Out test method) k was set to 7 in order to reach the minimum error rate : 3.3 %. {{0, 0, 1, 2 }, {0,100.0, 0.0, 0.0}, {1, 0.0, 96.0, 4.0}, {2, 0.0, 2.0, 98.0}} 9. Result of the Principal Component Analysis: The Principal Components Analysis is a very classical method in pattern recognition [Duda73]. PCA reduces the sample dimension in a linear way for the best representation in lower dimensions keeping the maximum of inertia. The best axe for the representation is however not necessary the best axe for the discrimination. After PCA, features are selected according to the percentage of initial inertia which is covered by the different axes and the number of features is determined according to the percentage of initial inertia to keep for the classification process. This selection method has been applied on the iris_CR database. When quasi-linear correlations exists between some initial features, these redundant dimensions are removed by PCA and this preprocessing is then recommended. In this case, before a PCA, the determinant of the data covariance matrix is near zero; this database is thus badly conditioned for all process which use this information (the quadratic classifier for example). The following files are available for the iris database: - ``iris_PCA.dat.Z'', the projection of the ``iris_CR'' database on its principal components (sorted in a decreasing order of the related inertia percentage; so, if you desire to work on the database projected on its x first principal components you only have to keep the x first attributes of the iris_PCA.dat database and the class labels (last attribute)). - ``iris_corr_circle.ps'', a graphical representation of the correlation between the initial attributes and the two first principal components, - ``iris_proj_PCA.ps'', a graphical representation of the projection of the initial database on the two first principal components, Table here below provides the inertia percentages associated to the eigenvalues corresponding to the principal component axis sorted in the decreasing order of their associated inertia percentage. Eigen Value Inertia Cumulated value percentage inertia 1 2.89141 72.8 72.8 2 0.91508 23.0 95.8 3 0.14637 3.7 99.5 4 0.02047 0.5 100.0 [Duda73] Duda, R.O. and Hart, P.E., Pattern Classification and Scene Analysis, John Wiley & Sons, 1973.