利用非线性时间结构的递归多核滤波器
Recursive Multikernel Filters Exploiting Nonlinear Temporal Structure
摘要：
在核方法中，通常通过使用时间延迟嵌入作为输入来包括关于数据的时间信息。最近，通过在再生核Hilbert空间中显式定义伽马滤波器，提出了一种替代公式，从而产生了一个复杂的模型，其中多个核对输入信号的不同时间组合进行操作。在原始公式中，然后简单地组合内核以获得单个内核矩阵（例如通过平均），这提供了计算优势，但丢弃了关于信号的时间结构的重要信息。受多核学习工作的启发，我们通过单独考虑不同的内核来克服这个缺点。我们提出了一种有效的策略，在训练阶段自适应地组合和选择这些内核。由此产生的批处理和在线算法自动学习处理从输入信号中提取的高度非线性的时间信息，这些信息隐式地编码在核值中。我们评估了我们的建议在几个人工和真实的任务，表明它可以优于经典的方法，在批量和在线设置。
英文摘要：
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert space, giving rise to a complex model where multiple kernels operate on different temporal combinations of the input signal. In the original formulation, the kernels are then simply combined to obtain a single kernel matrix (for instance by averaging), which provides computational benefits but discards important information on the temporal structure of the signal. Inspired by works on multiple kernel learning, we overcome this drawback by considering the different kernels separately. We propose an efficient strategy to adaptively combine and select these kernels during the training phase. The resulting batch and online algorithms automatically learn to process highly nonlinear temporal information extracted from the input signal, which is implicitly encoded in the kernel values. We evaluate our proposal on several artificial and real tasks, showing that it can outperform classical approaches both in batch and online settings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
