## Support Vector Machines for Analog Circuit Performance Representation (2003)

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Venue: | in Proceedings of DAC |

Citations: | 20 - 6 self |

### BibTeX

@INPROCEEDINGS{Bernardinis03supportvector,

author = {F. De Bernardinis and M. I. Jordan and A. Sangiovanni-Vincentelli},

title = {Support Vector Machines for Analog Circuit Performance Representation},

booktitle = {in Proceedings of DAC},

year = {2003},

pages = {964--969}

}

### OpenURL

### Abstract

The use of Support Vector Machines (SVMs) to represent the performance space of analog circuits is explored. In abstract terms, an analog circuit maps a set of input design parameters to a set of performance figures. This function is usually evaluated through simulations and its range defines the feasible performance space of the circuit. In this paper, we directly model performance spaces as mathematical relations. We study approximation approaches based on two-class and one-class SVMs, the latter providing a better tradeoff between accuracy and complexity avoiding "curse of dimensionality" issues with 2-class SVMs. We propose two improvements of the basic one-class SVM performances: conformal mapping and active learning. Finally we develop an efficient algorithm to compute projections, so that topdown methodologies can be easily supported.

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Citation Context ...1 νm s.t. w · xi ≥ ρ − ξi, ξi ≥ 0 � ξi − ρ} (5) As with two-class SVMs, there are efficient algorithms to solve this quadratic programming problem that exploit structural properties o=-=f SVMs, e.g. [9] [10]. -=-We based our implementation on libsvm [11], and we trained SVMs with up to 50,000 samples in very reasonable time (10’s of minutes). Differently from the two class formulation (3), there is no expli... |

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Citation Context ...er harmonic distortion, bandwidth and ripple in frequency response. Therefore, φLNA : R 7 → R 7 and PLNA : R 7 → {0, 1}. 4. SUPPORT VECTOR MACHINES Support Vector Machines were first proposed in =-=1992 [7]-=- to solve machine learning problems. Machine learning consists in classifying points in a large input space as satisfying a potentially complex unknown relation given a set of experiments that answer ... |

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Citation Context ... negatives (outliers). In Section 5.1 we rely on a standard two-class SVM classifiers to build an approximation for P. A more direct approach, however, is to make use of the so-called “one-class SVM=-=” [8]-=-. Since the characteristic functions of the performance relations being considered are deterministic, the support regions show sharp boundaries. The SVM approach also holds open the promise of obtaini... |

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Citation Context ...2 + 1 νm s.t. w · xi ≥ ρ − ξi, ξi ≥ 0 � ξi − ρ} (5) As with two-class SVMs, there are efficient algorithms to solve this quadratic programming problem that exploit structural properti=-=es of SVMs, e.g. [9] [-=-10]. We based our implementation on libsvm [11], and we trained SVMs with up to 50,000 samples in very reasonable time (10’s of minutes). Differently from the two class formulation (3), there is no ... |

69 |
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Citation Context ...Building an approximate representation of the performance space is of great interest for providing behavioral models with architectural constraints that can fully enable top-down design methodologies =-=[1]-=-. In the 70s and early 80s, a number of approaches [2] have been proposed to approximate the relation between circuit performance and parameters in explicit form. In particular, the design problem tac... |

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Citation Context ...inistic, the transition across the boundary should be sharp. One way to achieve improved resolution is via conformal transformation. This approach was described in the context of the two-class SVM by =-=[12]-=- and [13], but the basic idea is also applicable to the one-class SVM. In particular, an initial estimate of the boundary is provided by prior training of an SVM. Since support vectors are located on ... |

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Citation Context ...(5) As with two-class SVMs, there are efficient algorithms to solve this quadratic programming problem that exploit structural properties of SVMs, e.g. [9] [10]. We based our implementation on libsvm =-=[11], an-=-d we trained SVMs with up to 50,000 samples in very reasonable time (10’s of minutes). Differently from the two class formulation (3), there is no explicit penalties for false positives in (5) — a... |

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Citation Context ...mechanisms. A given performance figure is fit on a set of regressors that are function of physical parameters of the circuit. An interesting model based on boosting methods has been recently proposed =-=[5]-=-. However, regression approaches are not suited to top-down methodologies where abstraction levels introduce opaqueness in the system hierarchy that hides the implementation details needed for regress... |

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Citation Context ...s expressed as inequalities. Assuming that the region of points satisfying the requirements is convex, the boundaries of the region were approximated by a set of hyperplanes (simplicial approximation =-=[3]-=-) or by quadratic functions. If the exploration of the feasible region was part of an optimization procedure, the simplicial or quadratic approximation was refined locally to obtain a smaller error an... |

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Citation Context ...ehaviors and establishing cost and feasibility without further knowledge of the implementation architecture and topology. To cope with these problems, the Analog Platform concept has been proposed in =-=[4]-=- extending the one developed for the digital world. The term Analog Platform (AP) indicates an architectural resource to map analog functionalities during early system level exploration phases and con... |

13 |
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Citation Context ...the transition across the boundary should be sharp. One way to achieve improved resolution is via conformal transformation. This approach was described in the context of the two-class SVM by [12] and =-=[13]-=-, but the basic idea is also applicable to the one-class SVM. In particular, an initial estimate of the boundary is provided by prior training of an SVM. Since support vectors are located on the bound... |

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Citation Context ... figure is fitted independently from the others, so that errors in capturing relations among different feasible performances may cumulate. An approach to model the feasible space has been proposed in =-=[6]-=-. In this paper we present a novel approach to directly model performances that allows capturing high dimensional performance spaces with efficient representations and provides the necessary means to ... |

3 |
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Citation Context ...nce space is of great interest for providing behavioral models with architectural constraints that can fully enable top-down design methodologies [1]. In the 70s and early 80s, a number of approaches =-=[2]-=- have been proposed to approximate the relation between circuit performance and parameters in explicit form. In particular, the design problem tackled was to identify the value of the design parameter... |