摘要
This paper shows how a machine, which observes stimuli through an uncharacterized, uncalibrated channel and sensor, can glean machine-independent information (i.e., channel- and sensor-independent information) about the stimuli. This is possible if the following two conditions are satisfied by the observed stimulus and by the observing device, respectively: (1) the stimulus’ trajectory in the space of all possible configurations has a well-defined local velocity covariance matrix; (2) the observing device’s sensor state is invertibly related to the stimulus state. The first condition guarantees that the statistical properties of the stimulus time series endow the stimulus configuration space with a differential geometric structure (a metric and parallel transfer procedure), which can then be used to represent relative stimulus configurations in a coordinate-system-independent manner. This requirement is satisfied by a large variety of physical systems, and, in general, it is expected to be satisfied by stimulus trajecteries that densely cover stimulus state space and that have velocity distributions varying smoothly across that space. The second condition implies that the machine defines a specific coordinate system on the stimulus state space, with the nature of that coordinate system depending on the machine’s channels and detectors. Thus, machines with different channels and sensors “see” the same stimulus trajectory through state space, but in different machine-specific coordinate systems. It is shown that this requirement is almost certainly satisfied by any device that measures more than independent properties of the stimulus, where type=math/mml> d is the number of stimulus degrees of freedom. Taken together, the two conditions guarantee that the observing device can record the stimulus time series in its machine-specific coordinate system and then derive coordinate-system-independent (and, therefore, machine-independent) representations of relative stimulus configurations. The resulting description is an “inner” property of the stimulus time series in the sense that it does not depend on extrinsic factors such as the observer’s choice of a coordinate system in which the stimulus is viewed (i.e., the observer’s choice of channels and sensors). In other words, the resulting description is an intrinsic property of the evolution of the “real” stimulus that is “out there” broadcasting energy to the observer. This methodology is illustrated with analytic examples and with a numerically simulated experiment. In an intelligent sensory device, this kind of representation “engine” could function as a “front end” that passes channel- and sensor-independent stimulus representations to a pattern recognition module. After a pattern recognizer has been trained in one of these devices, it could be used without a change in other devices having different channels and sensors.
摘要译文
本文展示了如何通过未经表征的未校准通道和传感器观察刺激的机器如何收集与机器无关的信息（即，关于刺激的信道和传感器独立信息。如果观察到的刺激和观察装置满足以下两个条件，这是可能的，分别：（1）所有可能配置空间中的刺激轨迹具有明确定义的局部速度协方差矩阵;（2）观察装置的传感器状态与刺激状态可逆地相关。ndition保证刺激时间序列的统计特性赋予刺激配置空间差分几何结构（度量和并行传输过程），然后可以用它来表示与坐标系无关的方式的相对刺激配置。各种物理系统满足了这一要求，一般来说，人们期望通过密集地覆盖刺激状态空间并且具有在该空间上平滑变化的速度分布的刺激轨迹来满足它。第二个条件意味着机器在刺激状态空间上定义了一个特定的坐标系，具有该坐标系的性质取决于机器的通道和探测器。因此，具有不同通道和传感器的机器通过状态空间“看到”相同的刺激轨迹，但是在不同的机器专用坐标系中。结果表明，任何测量超过刺激的独立属性的设备几乎肯定满足了这个要求，其中type \x3d math / mml d是刺激自由度的数量。合在一起，这两个条件保证观测设备可以在其机器专用坐标系中记录刺激时间序列，然后导出与坐标系无关的（因此，机器无关的）相对刺激配置的表示。离子是刺激时间序列的“内在”属性，因为它不依赖于外在因素，例如观察者对观察刺激的坐标系的选择（即。例如，观察者选择的通道和传感器）。换一种说法，由此产生的描述是“真实”刺激的演变的内在属性，“真实”刺激是“在那里”向观察者广播能量。该方法用分析实例和数值模拟实验来说明。在智能感应设备中，这种表示“引擎”可以用作“前端”，其将通道和传感器独立的刺激表示传递给模式识别模块。在模式识别器已经在这些设备之一中训练之后，可以在不改变具有不同通道和传感器的其他设备的情况下使用它。
By David N. Levin[1;a)]. Channel-independent and sensor-independent stimulus representations[J]. Journal of Applied Physics, 2005,98(10): 104701