### Citations

5968 |
Classification and Regression Trees
- Breiman, Friedman, et al.
- 1984
(Show Context)
Citation Context ...r discriminant kernel to be utilized. With this simulated data set, all three techniques can be compared with the Bayes optimal classifier. The data set used was originally proposed by Breiman et al. =-=[23]-=- and is considered a difficult pattern recognition problem [19]. The waveforms that define each class are Class 1 Class 2 and Class 3 (19) is a number uniformly distributed over the interval (0, 1), i... |

4844 |
Pattern classification and scene analysis
- Duda, Hart
- 1973
(Show Context)
Citation Context ...ier to determine the class membership of an point vector . This is done using the training examples. The vector is not in the training set. Theoretically, this is accomplished via a decision function =-=[18]-=-. In practice, this is usually accomplished by extracting features from a standard TFR (e.g., the spectrogram) and classifying these features directly. This makes implicit assumptions about the amount... |

2803 |
Matrix computations
- Golub, Loan
- 1996
(Show Context)
Citation Context ...n performance and, thus, should be accounted for. More sophisticated techniques rank-order points in multiple feature dimensions (e.g., Fisher’s linear discriminant function [21] and Procrustes angle =-=[22]-=-). Ranking in this manner accounts for the potential gains afforded by exploiting the correlation in the selected points (features). Unfortunately, the number of points in the kernel is often greater ... |

2097 |
Information Theory and Reliable Communication
- Gallager
- 1968
(Show Context)
Citation Context ...dependent radar pulses were used, classification performance would improve. A simple approach would be to combine multiple pulses after the decision. Although this approach to combining is suboptimal =-=[31]-=-, using the Rihaczek or Wigner–Ville TFR with five pulses, the overall error rate would decrease to 0.0039 for Case 4 (assuming that out of five radar pulses, correctly classifying three, four, or fiv... |

468 | Regularized discriminant analysis’,
- Friedman
- 1989
(Show Context)
Citation Context ...curs most often when applying this technique to real-world data, where the number of examples is limited. This makes the estimated kernel values (i.e., linear discriminant weights) unreliable at best =-=[20]-=-. We propose an approach to cope with limited training examples. As a benefit, the classifier is not restricted to a linear discriminant function. This flexibility is incorporated into the overall str... |

214 | Discriminant analysis by Gaussian mixtures. - Hastie, Tibshirani - 1996 |

143 | Flexible discriminant analysis by optimal scoring. - Hastie, Tibshirani, et al. - 1994 |

115 |
Time-Frequency Analysis. Englewood Cliffs
- Cohen
- 1995
(Show Context)
Citation Context ...ed by an underlying function called a kernel. In past time-frequency research, kernels for a number of properties, such as finite-time support and minimizing quadratic interference, have been derived =-=[1]-=-. Although some of the resulting TFRs may offer advantages for classification of certain types of signals [2]–[4], the goal of sensitive detection or accurate classification is rarely an explicit goal... |

76 |
The Wigner distribution--A tool for time-frequency signal analysis--Part II: Discrete-time signals,
- Claasen, Mecklenbrauker
- 1980
(Show Context)
Citation Context ...ng TFR, which is the discrete version of the Rihaczek TFR [14], is given by (2) where is discrete frequency. The characteristic function [1] of the discrete Rihaczek TFR is simply . There is a kernel =-=[15]-=- that operates multiplicatively in both dimensions upon the auto-ambiguity function . The corresponding TFR is given by (3) The characteristic function of is . Any nonzero extent of in and/or can effe... |

59 |
Signal Energy distribution in Time and Frequency,”
- Rihaczek
- 1968
(Show Context)
Citation Context ...s autocorrelation function . This yields the auto-ambiguity function (1) where and are discrete Doppler and lag, respectively. The corresponding TFR, which is the discrete version of the Rihaczek TFR =-=[14]-=-, is given by (2) where is discrete frequency. The characteristic function [1] of the discrete Rihaczek TFR is simply . There is a kernel [15] that operates multiplicatively in both dimensions upon th... |

34 | Improved linear discrimination using time-frequency dictionaries.
- Buckheit, Donoho
- 1995
(Show Context)
Citation Context ...ns, this problem is ill posed. is often greater than the number of examples at our disposal. Buckheit and Donoho refer to this condition as the “neo-classical setting” of linear discriminant analysis =-=[19]-=-. This occurs most often when applying this technique to real-world data, where the number of examples is limited. This makes the estimated kernel values (i.e., linear discriminant weights) unreliable... |

34 |
Pattern Recognition and Prediction with Applications to Signal Characterization
- Kil, Shin
- 1996
(Show Context)
Citation Context ...ides a rank ordering of kernel points for classification. The main assumption of FDR is that the underlying probability distribution of each kernel location (feature) is Gaussian or at least unimodal =-=[21]-=-. If this assumption is satisfied, FDR is maximized when the separation between means of the class clusters is large and the within-class variance is small. Notice that if every location in the auto-a... |

24 | DiscreteTime, Discrete-Frequency Time-Frequency Representations,”
- Richman, Parks, et al.
- 1995
(Show Context)
Citation Context ...ormation in the original autoambiguity function. The TFRs that satisfy (7) are the class of regular TFRs defined by Hlawatsch [16]. One particular alternate candidate is the discrete Wigner–Ville TFR =-=[17]-=-. The Wigner–Ville transformation kernel is a modulating complex exponential. Hence, the Wigner–Ville TFR meets the requirements of (7). Classification performance will be equivalent to the Rihaczek T... |

24 |
Early detection of gear failure by vibration analysis, calculation of the time-frequency distribution”,
- WANG, MCFADDEN
- 1993
(Show Context)
Citation Context ...cations on the gearbox. Vibration patterns from these accelerometers are, in general, analyzed by using time-domain (e.g., [26]), frequency-domain (e.g., [27]), or combined time–frequency (e.g., [2], =-=[28]-=-) approaches. In the latter case, the application of time–frequency or related techniques have used standard TFRs that may degrade classification performance. Instead of imposing a priori smoothing in... |

22 |
A Signal Processing Technique for Detecting Local Defects in a Gear from the Signal Averaging of Vibration,’’
- McFadden, Smith
- 1985
(Show Context)
Citation Context ...ERENCES systems have been developed. Accelerometers are mounted at various locations on the gearbox. Vibration patterns from these accelerometers are, in general, analyzed by using time-domain (e.g., =-=[26]-=-), frequency-domain (e.g., [27]), or combined time–frequency (e.g., [2], [28]) approaches. In the latter case, the application of time–frequency or related techniques have used standard TFRs that may ... |

21 |
Application of orthogonal wavelets to early gear damage detection”,
- WANG, MCFADDEN
- 1995
(Show Context)
Citation Context ...us locations on the gearbox. Vibration patterns from these accelerometers are, in general, analyzed by using time-domain (e.g., [26]), frequency-domain (e.g., [27]), or combined time–frequency (e.g., =-=[2]-=-, [28]) approaches. In the latter case, the application of time–frequency or related techniques have used standard TFRs that may degrade classification performance. Instead of imposing a priori smooth... |

18 | Classification of underwater mammals using feature extraction based on timefrequency analysis and
- Huynh, Cooper, et al.
- 1998
(Show Context)
Citation Context ..., such as finite-time support and minimizing quadratic interference, have been derived [1]. Although some of the resulting TFRs may offer advantages for classification of certain types of signals [2]–=-=[4]-=-, the goal of sensitive detection or accurate classification is rarely an explicit goal of kernel design. Those few methods that propose to optimize the kernel for classification constrain the form of... |

18 | Optimal kernels of time-frequency representations for signal classification
- Davy, Doncarli
- 1998
(Show Context)
Citation Context ... that propose to optimize the kernel for classification constrain the form of the kernel to predefined parametric functions with symmetries that may not be germane to detection or classification [5], =-=[6]-=-. Manuscript received January 14, 1999; revised November 1, 2000. This work was supported by a the Office of Naval Research under Grant N00014-97-10082. The associate editor coordinating the review of... |

13 | Regularity and unitarity of bilinear time-frequency signal representations,
- Hlawatsch
- 1992
(Show Context)
Citation Context ...on for any candidate base TFR is that (7) for all and , preserving all information in the original autoambiguity function. The TFRs that satisfy (7) are the class of regular TFRs defined by Hlawatsch =-=[16]-=-. One particular alternate candidate is the discrete Wigner–Ville TFR [17]. The Wigner–Ville transformation kernel is a modulating complex exponential. Hence, the Wigner–Ville TFR meets the requiremen... |

12 |
Modular learning strategy for signal detection in a nonstationary environment
- Haykin, Bhattacharya
- 1997
(Show Context)
Citation Context ...ieve robust classification. The data is transformed to a standard TFR (e.g., the spectrogram or Wigner–Ville TFR [1]), and then, a projection of the TFR to a lower dimensional space is applied (e.g., =-=[7]-=-). This is shown in the top panel of Fig. 1. Using a standard TFR makes implicit a priori assumptions about the amount and type of time–frequency smoothing required for classification. This can potent... |

11 | Optimum time-frequency representations for the classification and detection of signals
- Heitz
- 1995
(Show Context)
Citation Context ...thods that propose to optimize the kernel for classification constrain the form of the kernel to predefined parametric functions with symmetries that may not be germane to detection or classification =-=[5]-=-, [6]. Manuscript received January 14, 1999; revised November 1, 2000. This work was supported by a the Office of Naval Research under Grant N00014-97-10082. The associate editor coordinating the revi... |

11 | Applications of operator theory to time-frequency analysis and classification
- McLaughlin
- 1997
(Show Context)
Citation Context ... classified via , where is an element-by-element product. Our approach to kernel design and classification is a generalization of the signal class-dependent method described in more detail before [9]–=-=[11]-=-. A brief overview of this previously described approach is provided as it is essential to understanding the motivations for our modifications. We extend the class-dependent methodology to a general k... |

11 |
Analysis of the Vibratory Excitation of Gear Systems: Basic Theory.
- Mark
- 1978
(Show Context)
Citation Context ...oped. Accelerometers are mounted at various locations on the gearbox. Vibration patterns from these accelerometers are, in general, analyzed by using time-domain (e.g., [26]), frequency-domain (e.g., =-=[27]-=-), or combined time–frequency (e.g., [2], [28]) approaches. In the latter case, the application of time–frequency or related techniques have used standard TFRs that may degrade classification performa... |

11 | Data-driven time-frequency classification techniques applied to tool-wear monitoring
- Gillespie, Atlas
- 2000
(Show Context)
Citation Context ...e correlation that exists between points in the auto-ambiguity plane. Finally, we mention that these techniques have recently been applied to tool-wear monitoring with interesting preliminary results =-=[32]-=-. An extension of this approach to unsupervised classification is also explored in that paper. ACKNOWLEDGMENT The authors would like to thank Dr. J. Droppo for his comments and suggestions during this... |

10 | Optimization of time and frequency resolution for radar transmitter identification - Gillespie, Atlas - 1998 |

9 | An Operator Theory Approach to Discrete Time-Frequency
- Narayanan, McLaughlin, et al.
- 1996
(Show Context)
Citation Context ...proach ascertains the necessary smoothing to achieve best classification performance. We present two optimality criteria and resulting algorithms that build on previous research in TFRs and operators =-=[8]-=-–[13]. To validate our approach, performance is demonstrated on simulated and real data. The simulated study shows our approach compares favorably with other techniques that have been benchmarked on t... |

7 |
Optimizing time-frequency distributions via operator theory
- Atlas, Droppo, et al.
- 1997
(Show Context)
Citation Context .... is classified via , where is an element-by-element product. Our approach to kernel design and classification is a generalization of the signal class-dependent method described in more detail before =-=[9]-=-–[11]. A brief overview of this previously described approach is provided as it is essential to understanding the motivations for our modifications. We extend the class-dependent methodology to a gene... |

6 | Time-frequency and time-scale techniques for the classification of native and bioprosthetic heart valve sounds - Bentley, Grant, et al. - 1998 |

5 |
Applications of classifier-optimal time-frequency distributions to speech analysis
- Droppo, Atlas
- 1998
(Show Context)
Citation Context ...ch ascertains the necessary smoothing to achieve best classification performance. We present two optimality criteria and resulting algorithms that build on previous research in TFRs and operators [8]–=-=[13]-=-. To validate our approach, performance is demonstrated on simulated and real data. The simulated study shows our approach compares favorably with other techniques that have been benchmarked on this d... |

2 |
The Westland helicopter report,”, http://wisdom.arl.psu.edu/Westland/welcome.htm
- Cameron
(Show Context)
Citation Context ... for detecting root fatigue, it would be best to have high resolution in frequency. Data provided by the Applied Research Laboratory (ARL) at Pennsylvania State University was used for classification =-=[29]-=-. These data were collected utilizing Westland Helicopters Ltd.’s Universal Transmission Test Rig to study a CH46 aft transmission. Faults were individually induced into the gearbox. Eight acceleromet... |

2 |
Time-frequency/time-scale analysis for navy radar applications,”, http://airborne.nrl.navy.mil/vchen/tftsa.html
- Chen
(Show Context)
Citation Context ...or transmitter identification, it would be best to have high resolution in frequency and little or no resolution in time. Data provided by the Naval Research Laboratory (NRL) is utilized in this work =-=[30]-=-. This data set contains ten radar pulses from four transmitters. This data comprises three tests from each of the four sources called A2, CCC2, F2, and H2. These will be denoted as class one through ... |