Segmentation of multivariate mixed data via lossy coding and compression In this paper, based on ideas from lossy data coding and compression, we present a simple but surprisingly effective technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions or linear subspaces. The goal is to find the optimal segmentation that minimizes the overall coding length of the segmented data, subject to a given distortion. We show that deterministic segmentation minimizes an upper bound on the (asymptotically) optimal solution. The proposed algorithm does not require any prior knowledge of the number or dimension of the groups, nor does it involve any parameter estimation. Simulation results reveal intriguing phasetransition behaviors of the number of segments when changing the level of distortion or the amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery and bioinformatic data.

Joint compressionclassification with quantizerclassifier dimension mismatch In this paper an algorithm is presented to design encoders that achieve good compression and classification. The goal is to minimize the classification error introduced by quantizing the data using encoders operating on low dimension inputs, which are subsets of the high dimension data used by the classifier for classification. In the encoder design information from the other dimensions of the vector is used to develop efficient encoders which are capable of achieving lower classification error for a given distortion. The design allows a tradeoff between distortion and classifications costs providing more flexibility in the overall system design. The algorithm is tested on Gaussian mixture data, which is classified using a classifier which takes as input vectors of quantized values. The proposed technique can trade performance to achieve lower complexity, which is desirable in devices having limited computational resources. For 4 dimensional Gaussian mixture data the misclassification was about 2.2% more than that achieved by using encoders of the same dimension as the classifier, while the encoding complexity was reduced by more than a factor of 2.