Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these approaches can be uncertain and produce results that differ from the planned budget, especially at the start of a project with limited data points. This paper proposes a constrained non-negative matrix completion model that predicts expenses by learning the likelihood of the project correlating with certain expense patterns in the latent space. The model is constrained on three probability simplexes, two of which are on the factor matrices and the third on the missing entries. Additionally, the predicted expense values are guaranteed to meet the budget constraint without the need of post-processing. An inexact alternating optimization algorithm is developed to solve the associated optimization problem and is proven to converge to a stationary point. Results from two real datasets demonstrate the effectiveness of the proposed method in comparison to state-of-the-art algorithms.

Tensor sparse coding (TSC) is a method used to excavate 3D volume structures extended by sparse coding (SC), which is increasingly applied in data noise attenuation. Existing TSC approaches control the intensity of noise attenuation by using a predetermined soft or hard threshold that relies on the noise variance. However, the noise variance in seismic data is unknown and varies with time and space, leading to the conventional TSC method not being able to track this change. To address this issue, we proposed a tensor sparse coding model with spatially adaptive coherent constraint (TSC-SAC) to find an optimal adjustable threshold without the demand for prior knowledge of the noise variance. The threshold is determined by the coherence of the residual with respect to the dictionary. Moreover, a tensor spatial coherence orthogonal matching pursuit algorithm (TSC-OMP) is developed for solving sparse representation. Unlike the existing threshold strategy in traditional TSC methods, TSC-OMP utilizes an ideal spatially adaptive coherence threshold to regulate the sparsity, which can effectively preserve the valuable information in processing for noise suppression. By comparing with four state-of-the-art denoising algorithms, we then demonstrated the superior performance of TSC-SAC on both a synthetic and two field data sets.INDEX TERMS Tensor sparse coding, spatially adaptive coherence threshold, tensor spatial coherence orthogonal matching pursuit (TSC-OMP).

The transfer learning between the source and target domain has already achieved significant success in machine learning areas. However, the existing methods can not achieve satisfactory result when solving the two distant domains transfer learning problem. In the worst case, it could lead to the negative transfer. In this paper, we propose a novel framework called transitive transfer sparse coding (TTSC) to solve the two distant domains transfer learning problem. On the one hand, as an extension of the sparse coding, the TTSC framework constructs a robust and high-level dictionary across three different domains and simultaneously obtains three good feature sparse representations. On the other hand, TTSC utilizes the intermediate domain as a strong bridge to transfer valuable knowledge between the source domain and target domain. Empirical studies validated that the TTSC framework significantly could outperform state-of-the-art methods.