Publications by Hans W. Borchers
Divisibility Rules Puzzle
Thanks to Florian W. Borchers for pointing out (and solving) this puzzle. The ‘divisibility rules’ puzzle Puzzle description Find a number M of 10 digits that satisfies the following conditions: The digits of M are all different, i.e each digit occurs exactly once, and: the number that forms the last two digits of M is divisible by 2, the...
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Subgroup Discovery
June 2020 Subgroup Discovery Systems Prof. Dr. Stefan Wrobel, Director of the Fraunhofer IAIS EXPLORA (Klösgen, 1996) MIDOS (Wrobel, 1997) MIDOS (Wrobel, 2001)Integrated in the Data Mining Tool KEPLER (Fa. Dialogis) VIKAMINE (Atzmüller, 2005)rsubgroup CRAN package pysubgroup (Python, pandas)KNIME, Orange (free)KEEL, RapidMiner (comm) Descri...
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Linear regression tree models
Introduction The idea of “Linear Regression Trees” is to grow a tree, similar to a decision tree, in which every end node is associated with linear regression for some or all of the variables in the data. The first idea and implementation was done by Ross Quinlan (of C4.5 fame) in his M5 program. The following packages contain implementations...
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Document
1.0 Parameterschätzung mit nls() Während lm() lineare ‘least-squares’ Regression behandelt, steht in Base R die Funktion nls() für nichtlineare Regression zur Verfügung. Siehe das Optimization Cheatsheet von J. Nash und H.W. Borchers. 1.1 Beispiel: Gedämpfte Schwingung Wir beginnen mit einem einfachen Beispiel, den künstlichen Daten ei...
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Document
Introduction A key-value store (in Computer Science often called associative array, or symbol table) is an abstract data type composed of a collection of (key, value) pairs, such that each possible key appears at most once in the collection. Many modern programming languages include associative arrays as primitive data types, or they are availabl...
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MLpackages
Introduction We will use Wine Quality data set from the UCI Machine Learning Repository. The “red wine” data span 1599 probes with 11 numerical attributes and one target attribute called quality. redwine = read.table("winequality-red.csv", header = TRUE, sep = ';') # redwine$quality = factor(redwine$quality) names(redwine) ## [1] "fixed.acid...
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ODE with R
Ordinary Differential Equation An ordinary Differential Equation (of first order) is an expression \[ y' = f(t, y) \] where \(y = y(t)\) is a function of the independent variable \(t\) (or \(x\)) defined on an interval/a time span \([t_0, t_1]\) and satisfies an initial condition \(y(t_0) = y_0\). Numerically the result shall be a vector (or ma...
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