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Last class introduced [kernel functions] trick as a key to make [SVM] an effective tool for classifying linearly separable data. Here we see some examples of kernel functions, and the condition that determined if these functions correspond to dot product in some feature space. | Last class introduced [kernel functions] trick as a key to make [SVM] an effective tool for classifying linearly separable data. Here we see some examples of kernel functions, and the condition that determined if these functions correspond to dot product in some feature space. | ||
| + | <math>\varphi:\Re^k\rightarrow\mathbb{H}</math> | ||
== Lectures == | == Lectures == | ||
[http://balthier.ecn.purdue.edu/index.php/Lecture_1_-_Introduction 1] [http://balthier.ecn.purdue.edu/index.php/Lecture_2_-_Decision_Hypersurfaces 2] [http://balthier.ecn.purdue.edu/index.php/Lecture_3_-_Bayes_classification 3] | [http://balthier.ecn.purdue.edu/index.php/Lecture_1_-_Introduction 1] [http://balthier.ecn.purdue.edu/index.php/Lecture_2_-_Decision_Hypersurfaces 2] [http://balthier.ecn.purdue.edu/index.php/Lecture_3_-_Bayes_classification 3] | ||
[http://balthier.ecn.purdue.edu/index.php/Lecture_4_-_Bayes_Classification 4] [http://balthier.ecn.purdue.edu/index.php/Lecture_5_-_Discriminant_Functions 5] [http://balthier.ecn.purdue.edu/index.php/Lecture_6_-_Discriminant_Functions 6] [http://balthier.ecn.purdue.edu/index.php/Lecture_7_-_MLE_and_BPE 7] [http://balthier.ecn.purdue.edu/index.php/Lecture_8_-_MLE%2C_BPE_and_Linear_Discriminant_Functions 8] [http://balthier.ecn.purdue.edu/index.php/Lecture_9_-_Linear_Discriminant_Functions 9] [http://balthier.ecn.purdue.edu/index.php/Lecture_10_-_Batch_Perceptron_and_Fisher_Linear_Discriminant 10] [http://balthier.ecn.purdue.edu/index.php/Lecture_11_-_Fischer%27s_Linear_Discriminant_again 11] [http://balthier.ecn.purdue.edu/index.php/Lecture_12_-_Support_Vector_Machine_and_Quadratic_Optimization_Problem 12] [http://balthier.ecn.purdue.edu/index.php/Lecture_13_-_Kernel_function_for_SVMs_and_ANNs_introduction 13] [http://balthier.ecn.purdue.edu/index.php/Lecture_14_-_ANNs%2C_Non-parametric_Density_Estimation_%28Parzen_Window%29 14] [http://balthier.ecn.purdue.edu/index.php/Lecture_15_-_Parzen_Window_Method 15] [http://balthier.ecn.purdue.edu/index.php/Lecture_16_-_Parzen_Window_Method_and_K-nearest_Neighbor_Density_Estimate 16] [http://balthier.ecn.purdue.edu/index.php/Lecture_17_-_Nearest_Neighbors_Clarification_Rule_and_Metrics 17] [http://balthier.ecn.purdue.edu/index.php/Lecture_18_-_Nearest_Neighbors_Clarification_Rule_and_Metrics%28Continued%29 18] | [http://balthier.ecn.purdue.edu/index.php/Lecture_4_-_Bayes_Classification 4] [http://balthier.ecn.purdue.edu/index.php/Lecture_5_-_Discriminant_Functions 5] [http://balthier.ecn.purdue.edu/index.php/Lecture_6_-_Discriminant_Functions 6] [http://balthier.ecn.purdue.edu/index.php/Lecture_7_-_MLE_and_BPE 7] [http://balthier.ecn.purdue.edu/index.php/Lecture_8_-_MLE%2C_BPE_and_Linear_Discriminant_Functions 8] [http://balthier.ecn.purdue.edu/index.php/Lecture_9_-_Linear_Discriminant_Functions 9] [http://balthier.ecn.purdue.edu/index.php/Lecture_10_-_Batch_Perceptron_and_Fisher_Linear_Discriminant 10] [http://balthier.ecn.purdue.edu/index.php/Lecture_11_-_Fischer%27s_Linear_Discriminant_again 11] [http://balthier.ecn.purdue.edu/index.php/Lecture_12_-_Support_Vector_Machine_and_Quadratic_Optimization_Problem 12] [http://balthier.ecn.purdue.edu/index.php/Lecture_13_-_Kernel_function_for_SVMs_and_ANNs_introduction 13] [http://balthier.ecn.purdue.edu/index.php/Lecture_14_-_ANNs%2C_Non-parametric_Density_Estimation_%28Parzen_Window%29 14] [http://balthier.ecn.purdue.edu/index.php/Lecture_15_-_Parzen_Window_Method 15] [http://balthier.ecn.purdue.edu/index.php/Lecture_16_-_Parzen_Window_Method_and_K-nearest_Neighbor_Density_Estimate 16] [http://balthier.ecn.purdue.edu/index.php/Lecture_17_-_Nearest_Neighbors_Clarification_Rule_and_Metrics 17] [http://balthier.ecn.purdue.edu/index.php/Lecture_18_-_Nearest_Neighbors_Clarification_Rule_and_Metrics%28Continued%29 18] | ||
Revision as of 10:35, 23 March 2008
(continued from [Lecture 12])
[Kernel Functions]
===========
Main article: [Kernel Functions]
Last class introduced [kernel functions] trick as a key to make [SVM] an effective tool for classifying linearly separable data. Here we see some examples of kernel functions, and the condition that determined if these functions correspond to dot product in some feature space.
$ \varphi:\Re^k\rightarrow\mathbb{H} $
