Storage and transmission requirements for hyperspectral data sets are significant. To reduce hardware costs, well-designed compression techniques are needed to preserve information content while maximizing compression ratios. Lossless compression techniques maintain data integrity, but yield small compression ratios. We present a slightly lossy compression algorithm that uses the noise statistics of the data to preserve information content while maximizing compression ratios. The adaptive principal components analysis (APCA) algorithm uses noise statistics to determine the number of significant principal components and selects only those that are required to represent each pixel to within the noise level. We demonstrate the effectiveness of these methods with airborne visible/infrared spectrometer (AVIRIS), hyperspectral digital imagery collection experiment (HYDICE), hyperspectral mapper (HYMAP), and Hyperion datasets.