**Robust Multiple Signal Classification (MUSIC)**

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on the observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: 1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and 2) under the assumption of spherically contoured noise distribution, the noise subspace can be determined from the eigendecomposition of the MT-covariance. Furthermore, we derive a new robust measure-transformed minimum description length (MDL) criterion for estimating the number of signals, and extend the MT-MUSIC framework to the case of coherent signals. The proposed approach is illustrated in simulation examples that show its advantages as compared to other robust MUSIC and MDL generalizations. … **Cumulative Gains Model Quality Metric**

In developing risk models, developers employ a number of graphical and numerical tools to evaluate the quality of candidate models. These traditionally involve numerous measures including the KS statistic or one of many Area Under the Curve (AUC) methodologies on ROC and cumulative Gains charts. Typical employment of these methodologies involves one of two scenarios. The first is as a tool to evaluate one or more models and ascertain the effectiveness of that model. Second however is the inclusion of such a metric in the model building process itself such as the way Ferri et al. proposed to use Area Under the ROC curve in the splitting criterion of a decision tree. However, these methods fail to address situations involving competing models where one model is not strictly above the other. Nor do they address differing values of end points as the magnitudes of these typical measures may vary depending on target definition making standardization difficult. Some of these problems are starting to be addressed. Marcade Chief Technology officer of the software vendor KXEN gives an overview of several metric techniques and proposes a new solution to the problem in data mining techniques. Their software uses two statistics called KI and KR. We will examine the shortfalls he addresses more thoroughly and propose a new metric which can be used as an improvement to the KI and KR statistics. Although useful in a machine learning sense of developing a model, these same issues and solutions apply to evaluating a single model’s performance as related by Siddiqi and Mays with respect to risk scorecards. We will not specifically give examples of each application of the new statistics but rather make the claim that it is useful in most situations where an AUC or model separation statistic (such as KS) is used. … **Probabilistic D-Clustering**

We present a new iterative method for probabilistic clustering of data. Given clusters, their centers and the distances of data points from these centers, the probability of cluster membership at any point is assumed inversely proportional to the distance from (the center of) the cluster in question. This assumption is our working principle. The method is a generalization, to several centers, of theWeiszfeld method for solving the Fermat-Weber location problem. At each iteration, the distances (Euclidean, Mahalanobis, etc.) from the cluster centers are computed for all data points, and the centers are updated as convex combinations of these points, with weights determined by the above principle. Computations stop when the centers stop moving. Progress is monitored by the joint distance function, a measure of distance from all cluster centers, that evolves during the iterations, and captures the data in its low contours. The method is simple, fast (requiring a small number of cheap iterations) and insensitive to outliers. …

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**19**
*Friday*
Jan 2018

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