Remote classification involves offloading complex object-recognition tasks from mobile devices to servers at the network edge. It brings to the mobile device the capability of discerning hundreds of object classes by using the computational and storage capabilities of the infrastructure. Remote classification is challenged by the finite and variable data rate of the wireless channel, which affects the capability to transfer high-dimensional features and thus limits the classification resolution. We introduce a set of metrics under the name of classification capacity that are defined as the maximum number of classes that can be discerned over a given communication channel while meeting a target probability for classification error. We treat both the cases of a channel where the instantaneous rate is known and unknown. The objective is to choose a subset of classes from a class library that offers satisfactory performance over a given channel. We treat two different cases of subset selection. First, a device can select the subset by pruning the class library until arriving at a subset that meets the targeted error probability while maximizing the classification capacity. Adopting a subspace data model, we prove the equivalence of classification capacity maximization to the problem of packing on the Grassmann manifold. The results show that the classification capacity grows exponentially with the instantaneous communication rate, and super-exponentially with the dimensions of each data cluster. This also holds for ergodic and outage capacities with fading if the instantaneous rate is replaced with an average rate and a fixed rate, respectively. In the second case, a device has a unique preference of class subset for every communication rate, which is modeled as an instance of uniformly sampling the library. Without class selection, the classification capacity and its ergodic and outage counterparts are proved to scale linearly with their corresponding communication rates instead of the exponential growth in the last case.

中文翻译：

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无线信道远程分类能力

远程分类涉及将复杂的对象识别任务从移动设备卸载到网络边缘的服务器。它通过使用基础设施的计算和存储能力为移动设备带来了识别数百个对象类别的能力。远程分类受到无线信道有限且可变的数据速率的挑战，这会影响传输高维特征的能力，从而限制分类分辨率。我们在名称下引入了一组指标分类容量定义为在满足分类错误的目标概率的同时，在给定的通信信道上可以识别的最大类别数。我们处理瞬时速率已知和未知的两种情况。目标是从类库中选择在给定通道上提供令人满意的性能的类子集。我们处理子集选择的两种不同情况。首先，设备可以通过修剪类库来选择子集，直到达到满足目标错误概率的子集，同时最大化分类容量。采用子空间数据模型，我们证明了分类容量最大化与 Grassmann 流形上的打包问题的等价性。结果表明分类容量增长与瞬时通信速率呈指数关系，并且 与每个数据簇的维度超指数。如果瞬时速率分别替换为平均速率和固定速率，这也适用于具有衰落的遍历和中断容量。在里面第二种情况，设备对每个通信速率都有一个独特的类子集偏好，这被建模为对库进行均匀采样的实例。没有类选择，分类能力及其遍历和中断对应物被证明是可扩展的与它们相应的通信速率呈线性关系，而不是在最后一种情况下呈指数增长。