Distributed Principal Component Analysis with Limited Communication - Experiments Experiments are on a 1000 x 200 Gaussian data matrix, and show the effects of performing Riemannian gradient descent from a uniformly random initialization point on the unit sphere, using the following quantization methods: • Full precision : gradients are communicated at full (32 bit) precision. • Euclidean gradient difference quantization : differences in each worker ’ s Euclidean gradients from the last epoch to the current epoch are quantized and averaged, from which the other workers can reconstruct esti- mates a common estimate of the average gradient (since this improves performance over quantizing the gra- dients themselves). Quantization is by coordinate - wise rounding. • Riemannian gradient quantization (the paper ’ s method): each worker ’ s Riemannian gradient is quantized (one cannot quantize differences as above, since the tangent space in question changes every epoch). Quan- tization is by coordinate - wise rounding under a random basis of the current tangent space. The number of bits used per coordinate for the quantized methods is given in figure titles. The experiments show that the paper ’ s approach of quantizing Riemannian gradients in the tangent space provides significantly better con- vergence than the naïve approach of quantizing (differences of) Euclidean gradients, and approaches the perfor- mance of the full - precision method using only 2 - 4 bits per coordinate.