Applications such as scientific simulations and power grid monitoring are generating so much data quickly that compression is essential to reduce storage requirement or transmission capacity. To achieve better compression, one is often willing to discard some repeated information. These lossy compression methods are primarily designed to minimize the Euclidean distance between the original data and the compressed data. But this measure of distance severely limits either reconstruction quality or compression performance. We propose a new class of compression method by redefining the distance measure with a statistical concept known as exchangeability. This approach reduces the storage requirement and captures essential features, while reducing the storage requirement. In this paper, we report our design and implementation of such a compression method named IDEALEM. To demonstrate its effectiveness, we apply it on a set of power grid monitoring data, and show that it can reduce the volume of data much more than the best known compression method while maintaining the quality of the compressed data. In these tests, IDEALEM captures extraordinary events in the data, while its compression ratios can far exceed 100.