多野值混合线性模型的中值K-平坦
Median K-flats for hybrid linear modeling with many outliers
摘要：
我们描述了中值K-Flats（MKF）算法，这是一种用于混合线性建模的简单在线方法，即，用于通过平坦的混合来近似数据。该算法在对数据进行聚类的同时，寻找其对应的最佳l1 d平坦逼近，从而使累积l1误差最小化。当前的实现将d-平坦限制为d维线性子空间。它所需的存储量可以忽略不计，并且当建模由D维欧氏空间中的N个点和K个d维线性子空间组成的数据时，其复杂度为O（n K d D+n d^2 D），其中n是收敛所需的迭代次数（经验上为10^4的数量级）。由于它是一个在线算法，数据可以增量地提供给它，它可以增量地产生相应的输出。该算法的性能仔细评估使用合成和真实的数据。
英文摘要：
We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their corresponding best approximating l1 d-flats, so that the cumulative l1 error is minimized. The current implementation restricts d-flats to be d-dimensional linear subspaces. It requires a negligible amount of storage, and its complexity, when modeling data consisting of N points in D-dimensional Euclidean space with K d-dimensional linear subspaces, is of order O(n K d D+n d^2 D), where n is the number of iterations required for convergence (empirically on the order of 10^4). Since it is an online algorithm, data can be supplied to it incrementally and it can incrementally produce the corresponding output. The performance of the algorithm is carefully evaluated using synthetic and real data.
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