The paper introduces the fused lasso, an extension of the lasso method for regression problems where features can be ordered in a meaningful way. The lasso penalizes the sum of absolute values of coefficients to encourage sparsity, while the fused lasso adds a penalty on the differences between consecutive coefficients, promoting both sparsity in coefficients and their differences, i.e., local constancy. This is particularly useful when the number of features p is much larger than the sample size N. The method is extended to the hinge loss function used in support vector classifiers. The paper illustrates the method on protein mass spectroscopy and gene expression data. It discusses computational methods, asymptotic properties, and comparisons with other techniques like soft thresholding and wavelets. The fused lasso is shown to perform well in estimating true coefficients and handling high-dimensional data. The paper also addresses the degrees of freedom of the fused lasso fit and its sparsity properties. A simulation study and application to leukemia classification using microarray data are presented, demonstrating the effectiveness of the fused lasso in various scenarios. The method is also applied to unordered features by estimating an order from the data. The paper concludes with a discussion of computational challenges and potential extensions to higher-dimensional problems.The paper introduces the fused lasso, an extension of the lasso method for regression problems where features can be ordered in a meaningful way. The lasso penalizes the sum of absolute values of coefficients to encourage sparsity, while the fused lasso adds a penalty on the differences between consecutive coefficients, promoting both sparsity in coefficients and their differences, i.e., local constancy. This is particularly useful when the number of features p is much larger than the sample size N. The method is extended to the hinge loss function used in support vector classifiers. The paper illustrates the method on protein mass spectroscopy and gene expression data. It discusses computational methods, asymptotic properties, and comparisons with other techniques like soft thresholding and wavelets. The fused lasso is shown to perform well in estimating true coefficients and handling high-dimensional data. The paper also addresses the degrees of freedom of the fused lasso fit and its sparsity properties. A simulation study and application to leukemia classification using microarray data are presented, demonstrating the effectiveness of the fused lasso in various scenarios. The method is also applied to unordered features by estimating an order from the data. The paper concludes with a discussion of computational challenges and potential extensions to higher-dimensional problems.