论文标题
无监督的光谱频段特征识别以进行最佳过程歧视
Unsupervised spectral-band feature identification for optimal process discrimination
论文作者
论文摘要
现实世界动态过程的变化通常用能量的差异来描述，$ \ textbf {e}（\suesperlineallineallinealllineα）$的一组频谱波段$ \ usevenlinelineLineLlineLlinellineα$。 Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underlineα \subset \ Mathbb {r}^+$，使得能量$ \ textbf {e}（\suesslineα）$的这些频段可以最佳区分两类。我们介绍了Ego-MDA，这是一种无监督的方法，用于识别两个类别的光谱样品的最佳光谱$ \ usewissin^*$。 EGO-MDA采用统计方法，迭代地将调整后的多项式日志类（偏差）标准$ \ MATHCAL {d}（\Underlineα，\ Mathcal {M Mathcal {M}）$最小化。 Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underlineα, \mathcal{M})$ and identify a classifier that optimally为给定的光谱表示区分两个类别。有效的全局优化（EGO）找到了频谱$ \upslineα^* = \ underSet {\liseplineα} {\ rm argmin}〜\ mathcal {d}（\useverlineα，\ mathcal {m Mathcal {m}对于混合物和模型错误指定之间低分离的病理案例，我们讨论了样本量和迭代次数对参数估计值$ \ MATHCAL {M} $的效果，因此分类器的性能。提供了有关合成数据集的案例研究。在用于异常跟踪的最佳光谱伴随的工程应用中，相对于其他测试的其他方法，EGO-MDA的中位偏差至少提高了70％。
Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underlineα)$ of a set of spectral-bands $\underlineα$. Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underlineα \subset \mathbb{R}^+$ such that the energies $\textbf{E}(\underlineα)$ of these bands can optimally discriminate between the two classes. We introduce EGO-MDA, an unsupervised method to identify optimal spectral-bands $\underlineα^*$ for given samples of spectra from two classes. EGO-MDA employs a statistical approach that iteratively minimizes an adjusted multinomial log-likelihood (deviance) criterion $\mathcal{D}(\underlineα,\mathcal{M})$. Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underlineα, \mathcal{M})$ and identify a classifier that optimally discriminates between two classes for a given spectral representation. The Efficient Global Optimization (EGO) finds the spectral-bands $\underlineα^* = \underset{\underlineα}{\rm argmin}~\mathcal{D}(\underlineα,\mathcal{M})$ for given GMM parameters $\mathcal{M}$. For pathological cases of low separation between mixtures and model misspecification, we discuss the effect of the sample size and the number of iterations on the estimates of parameters $\mathcal{M}$ and therefore the classifier performance. A case study on a synthetic data set is provided. In an engineering application of optimal spectral-banding for anomaly tracking, EGO-MDA achieved at least 70% improvement in the median deviance relative to other methods tested.
