![]() A different word (eilikrines) is used in 2 Peter 3:1, the Revised Version (British and American) "sincere." "Purity" (hagneia) occurs only in the King James Version in 1 Timothy 4:12 1 Timothy 5:2 in the Revised Version (British and American) in 2 Corinthians 11:3 (as the translation of tes hagnotelos). alkali for soap) in Isaiah 1:25, the Revised Version (British and American) "thoroughly (margin "as with lye," the King James Version "purely") purge away thy dross" "pureness" is the King James Version translation of the same word in Job 22:30, the Revised Version (British and American) "cleanness." In the New Testament "pure" is the translation chiefly of katharos ( Matthew 5:8, Blessed are the pure in heart," etc.), but also of hagnos ( Philippians 4:8 1 Timothy 5:22 James 3:17 1 John 3:3 -always in an ethical sense). ![]() "Pure" in the Old Testament represents many Hebrew words, most frequently Tahor "purely," occurs once only in the King James Version, as the translation of bor, properly "that which cleanses" (compare Job 9:30, the Revised Version margin "Hebrew `cleanse my hands with lye,' " i.e. Pur, pur'-li, pu'-ri-ti: This group of words has in the Old Testament and the New Testament an almost exclusively ethical significance, though the word "pure" is of course used also in its literal sense of freedom from alloy or other alien matter ( Exodus 25:11, etc.). I am not sure what you mean by important, but in both cases we try to split S so that the "overall purity" of $S_1.,S_k$ is highest, so i would say that purity is equally important in both kinds of decision trees.International Standard Bible Encyclopedia PURE PURELY PURITY ![]() Is purity more important in classification than in regression analysis? I think that wikipedia's explanation about Gini index, as well as the answers to this Quora question should answer your last question (about Gini index). Gini index is one of the popular measures of impurity, along with entropy, variance, MSE and RSS. the most important part of such algorithms - deciding how to split $S$ - is determined by purity. The root is the test, and its sons are calculated by recursively calling the algorithm for each of $S_1.,S_k$. Return a tree whose root has $k$ sons.the average purity of $S_1.,S_k$ is highest). Otherwise, find a test that examines a feature (or multiple features) and divides $S$ accordingly into disjoint sets $S_1.,S_k$, such that their "overall purity" is highest (e.g.If $S$ is pure enough, return a single-node tree, labeled with the most common class in $S$ (or with the average of target values in $S$, in case of a regression tree).Most of these algorithms use a process called top-down induction of decision trees (TDIDT), and look roughly like this: So people came up with such more efficient algorithms, and some of them are based on measures of impurity. any algorithm that is guaranteed to find the optimal decision tree is inefficient (assuming $P \ne NP$, which is still unknown), but algorithms that don't guarantee that might be more efficient. The problem of learning an optimal decision tree is known to be $NP$-complete Similarly, if the target variables of the examples are very close to each other, then the set's purity is quite high. If the color of most of the pixels is very close to purple, you would say that the picture is almost pure purple.You can think of a set of examples as the set of pixels in a picture that should contain just a single color, while the value of a target variable (of an example) is like a color on the continuous color spectrum. The gist of the idea of purity is quite the same here (which is fortunate, as I am afraid this analogy is less natural). So the purity of a set of examples is the homogeneity of its examples - with regard to their classes. Similarly, if the examples are split evenly between all of the classes, then the set's purity is lowest. If 1/3 of the atoms were gold, 1/3 silver, and 1/3 iron - you would say that for a ball made of 3 kinds of atoms, its purity is lowest.Similarly, if all of the examples in the set were of the same class, then the set's purity would be highest. If all of the ball's atoms were gold - you would say that the ball is purely gold, and that its purity level is highest (and its impurity level is lowest).Intuitively, you can think of a set of examples as the set of atoms in a metallic ball, while the class of an example is like the kind of an atom (e.g. What is node impurity/purity in decision trees? Classification Trees
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