#### DMCA

## RIDGE-ADJUSTED SLACK VARIABLE OPTIMIZATION FOR SUPERVISED CLASSIFICATION

### Citations

2379 |
An Introduction to Support Vector Machines and Other Kernel-based Learning Methods
- Cristianini, Shawe-Taylor
- 2000
(Show Context)
Citation Context ...s: adult, bank and shuttle. [5] The only preprocessing is to normalize each feature with its maximum value. In this section, we show the results obtained by sequential RiSVO and compare them with SVM =-=[15]-=- implemented by SVMlight [16]. Moreover, the results of parallel RiSVO is simulated by an independent sequential process. More results obtained by tuning some of the parameters can be found in Figure ... |

1859 | Making large–scale SVM learning practical
- Joachims
- 1999
(Show Context)
Citation Context ...5] The only preprocessing is to normalize each feature with its maximum value. In this section, we show the results obtained by sequential RiSVO and compare them with SVM [15] implemented by SVMlight =-=[16]-=-. Moreover, the results of parallel RiSVO is simulated by an independent sequential process. More results obtained by tuning some of the parameters can be found in Figure 3. Data Parameter Adult ρ = 0... |

953 |
Ridge regression: biased estimation for non-orthogonal problems
- HOERL, R
- 1970
(Show Context)
Citation Context ... conclude that Jk∗SS ≥ J (k+1)∗SS . Since this holds for all k, the sequence J1SS , J 2 SS , · · · , JKSS is monotonically decreasing to a minimum value. 3.3. Ridge-adjusted extension The Ridge trace =-=[10, 11]-=- in regression techniques penalizes the size of the regression coefficients and therefore helps with overfitting problems. In this section, ridge-adjusted extension of the algorithm is presented. This... |

685 |
Learning with Kernels: Support Vector
- Schölkopf, Smola
- 2002
(Show Context)
Citation Context ...(5) we can find α = [aT , b]T as follows: α∗ = [ a∗ b∗ ] = γ [K, e] + tS (6) where K is the kernel matrix, whose entries are defined by a user chosen kernel function k(x, y), such that Kij = k(xi,xj) =-=[6, 7, 8, 9]-=-. Vector e is a column vector with all ones and tS is the vector containing all targets t(i), for xi ∈ S. Let us call “the set which is not active” at step k the “complementary set” and denote it as S... |

53 |
UCI Machine Learning Repository [http://archive.ics.uci.edu/ml].
- Lichman
- 2013
(Show Context)
Citation Context ...f Sall and Gl+1 to be a subset of Sall/(G1 ∪ · · · ∪ Gl), ∀l = 1, · · · , L− 1. 5. EXPERIMENTAL RESULTS We have conducted simulations studies on three standard UCI data sets: adult, bank and shuttle. =-=[5]-=- The only preprocessing is to normalize each feature with its maximum value. In this section, we show the results obtained by sequential RiSVO and compare them with SVM [15] implemented by SVMlight [1... |

22 | A geometric approach to support vector machine (SVM) classification,”
- Mavroforakis, Theodoridis
- 2006
(Show Context)
Citation Context ...t of performance over the SVM classifier. Index Terms— slack energy minimization, kernel method, ridge-regression, classification, training data selection 1. INTRODUCTION Support Vector Machine (SVM) =-=[1, 2]-=- is the optimal classifier in terms of the maximum margin between two classes. Classification techniques by Mean Squared Slack (MSS) minimization are closely related to SVM. The relation has been desc... |

15 | Extension of Wirtinger’s calculus to reproducing kernel Hilbert spaces and the complex kernel LMS,”
- Bouboulis, Theodoridis
- 2011
(Show Context)
Citation Context ...(5) we can find α = [aT , b]T as follows: α∗ = [ a∗ b∗ ] = γ [K, e] + tS (6) where K is the kernel matrix, whose entries are defined by a user chosen kernel function k(x, y), such that Kij = k(xi,xj) =-=[6, 7, 8, 9]-=-. Vector e is a column vector with all ones and tS is the vector containing all targets t(i), for xi ∈ S. Let us call “the set which is not active” at step k the “complementary set” and denote it as S... |

2 |
Statistical Learning Theory, 1st Edition, Wiley-Interscience
- Vapnik
- 1998
(Show Context)
Citation Context ...t of performance over the SVM classifier. Index Terms— slack energy minimization, kernel method, ridge-regression, classification, training data selection 1. INTRODUCTION Support Vector Machine (SVM) =-=[1, 2]-=- is the optimal classifier in terms of the maximum margin between two classes. Classification techniques by Mean Squared Slack (MSS) minimization are closely related to SVM. The relation has been desc... |

2 |
Online classification using kernels and projection-based adaptive algorithms
- Slavakis, Theodoridis, et al.
- 2008
(Show Context)
Citation Context ...(5) we can find α = [aT , b]T as follows: α∗ = [ a∗ b∗ ] = γ [K, e] + tS (6) where K is the kernel matrix, whose entries are defined by a user chosen kernel function k(x, y), such that Kij = k(xi,xj) =-=[6, 7, 8, 9]-=-. Vector e is a column vector with all ones and tS is the vector containing all targets t(i), for xi ∈ S. Let us call “the set which is not active” at step k the “complementary set” and denote it as S... |

2 |
Bouboulis P., Theodoridis S., Online Learning in Reproducing Kernel Spaces. E-reference for Signal Processing
- Slavakis
- 2013
(Show Context)
Citation Context |

2 |
Ridge regression and its application to medical data
- Jain
- 1985
(Show Context)
Citation Context ... conclude that Jk∗SS ≥ J (k+1)∗SS . Since this holds for all k, the sequence J1SS , J 2 SS , · · · , JKSS is monotonically decreasing to a minimum value. 3.3. Ridge-adjusted extension The Ridge trace =-=[10, 11]-=- in regression techniques penalizes the size of the regression coefficients and therefore helps with overfitting problems. In this section, ridge-adjusted extension of the algorithm is presented. This... |

1 |
Binary Classification By Minimizing the
- Diamantaras, Kotti
- 2012
(Show Context)
Citation Context ...classifier in terms of the maximum margin between two classes. Classification techniques by Mean Squared Slack (MSS) minimization are closely related to SVM. The relation has been described in detail =-=[3, 4]-=- . In the previous work, a classification technique called Slackmin is presented. This approach attempts to minimize the MSS, which yields a much simpler computation compared to SVM for big data scena... |

1 |
Towards Minimizing the Energy of Slack Variables for Binary Classification, Proceeding of 20th EUSIPCO
- Kotti, Diamantaras
- 2012
(Show Context)
Citation Context ...classifier in terms of the maximum margin between two classes. Classification techniques by Mean Squared Slack (MSS) minimization are closely related to SVM. The relation has been described in detail =-=[3, 4]-=- . In the previous work, a classification technique called Slackmin is presented. This approach attempts to minimize the MSS, which yields a much simpler computation compared to SVM for big data scena... |

1 |
CloudSVM: Training an SVM Classifier
- Catak, Balaban
- 2013
(Show Context)
Citation Context ...de in this context. There are two steps in this framework: Map (dividing the work) and Reduce (merging the results). Many machine learning techniques adopt this concept to cope with big data problems =-=[14, 13]-=-. Fig. 2. MapReduce for parallel RiSVO. The data set is divided into L nodes. Each node carries out 1L of the computation. The solutions computed from all the nodes are then combined in a linear fashi... |