We propose a new method ? Cubic Higher-order Local Auto-Correlation (CHLAC) ? to address three-way data analysis. This method is a natural extension of Higherorder Local Auto-Correlation (HLAC) [6], which deals only with two-way data. Both methods use "correlation" to summarize relative positions or motions within a local data region, and these can be calculated simply with a low computational load. Moreover, our new method (CHLAC) offers several preferable properties as well as HLAC: shiftinvariance to data (rendering the method segmentationfree), additivity for data, and robustness to noise in data. In this study, we applied this method to action and simultaneous multiple-person identification from a motion-image sequence through the property of data additivity. Experimental results showed that this method performed well.