Sentences with HYPERPLANE

"A hyperplane is a subspace of one dimension lower than its ambient space."

"In geometric language, a hyperplane divides an n-dimensional space into two half-spaces."

"The concept of a hyperplane is used in linear algebra and geometry."

"A hyperplane in two-dimensional space is simply a line."

"The graph of a linear equation represents a hyperplane."

"The equation 2x + 3y = 6 represents a hyperplane in 2-dimensional space."

"In SVM (support vector machines), a hyperplane is used to separate classes of data."

"The decision boundary in logistic regression is a hyperplane."

"By adding more constraints, an optimization problem can be transformed into a problem of constrained optimization on a hyperplane."

"In binary classification, a hyperplane is used to divide data into two classes."

"A hyperplane can also be defined as the set of overall feature vectors where the decision function is zero."

"In machine learning, hyperplanes are commonly used in classification algorithms."

"Linear regression attempts to find the best-fit hyperplane for a given dataset."

"Neural networks use hyperplanes to separate data into distinct regions."

"Random forests can combine the predictions of multiple hyperplanes."

"The concept of a hyperplane extends to higher dimensions."

"In three-dimensional space, a hyperplane is a two-dimensional subspace."

"In four-dimensional space, a hyperplane is a three-dimensional subspace."

"The hyperplane separates points on one side from points on the other side."

"The concept of a hyperplane is fundamental in many areas of mathematics and computer science."