Simultaneously Structured Models with Application to Sparse and Low-rank Matrices

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank matrices, among others. In various applications in signal processing and machine learning, the model of interest is known to be structured in several ways at the same time, for example, a matrix that is simultaneously sparse and low-rank. Often norms that promote each individual structure are known, and allow for recovery using an order-wise optimal number of measurements (e.g., $\ell_1$ norm for sparsity, nuclear norm for matrix rank). Hence, it is reasonable to minimize a combination of such norms. We show that, surprisingly, if we use multi-objective optimization with these norms, then we can do no better, order-wise, than an algorithm that exploits only one of the present structures. This result suggests that to fully exploit the multiple structures, we need an entirely new convex relaxation, i.e. not one that is a function of the convex relaxations used for each structure. We then specialize our results to the case of sparse and low-rank matrices. We show that a nonconvex formulation of the problem can recover the model from very few measurements, which is on the order of the degrees of freedom of the matrix, whereas the convex problem obtained from a combination of the $\ell_1$ and nuclear norms requires many more measurements. This proves an order-wise gap between the performance of the convex and nonconvex recovery problems in this case. Our framework applies to arbitrary structure-inducing norms as well as to a wide range of measurement ensembles. This allows us to give performance bounds for problems such as sparse phase retrieval and low-rank tensor completion.Comment: 38 pages, 9 figure

Temperature-dependent development of the two-spotted ladybeetle, Adalia bipunctata, on the green peach aphid, Myzus persicae, and a factitious food under constant temperatures

The ability of a natural enemy to tolerate a wide temperature range is a critical factor in the evaluation of its suitability as a biological control agent. In the current study, temperature-dependent development of the two-spotted ladybeetle A. bipunctata L. (Coleoptera: Coccinellidae) was evaluated on Myzus persicae (Sulzer) (Hemiptera: Aphididae) and a factitious food consisting of moist bee pollen and Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) eggs under six constant temperatures ranging from 15 to 35 degrees C. On both diets, the developmental rate of A. bipunctata showed a positive linear relationship with temperature in the range of 15-30 degrees C, but the ladybird failed to develop to the adult stage at 35 degrees C. Total immature mortality in the temperature range of 15-30 degrees C ranged from 24.30-69.40% and 40.47-76.15% on the aphid prey and factitious food, respectively. One linear and two nonlinear models were fitted to the data. The linear model successfully predicted the lower developmental thresholds and thermal constants of the predator. The non-linear models of Lactin and Briere overestimated the upper developmental thresholds of A. bipunctata on both diets. Furthermore, in some cases, there were marked differences among models in estimates of the lower developmental threshold (t(min)). Depending on the model, t(min) values for total development ranged from 10.06 to 10.47 degrees C and from 9.39 to 11.31 degrees C on M. persicae and factitious food, respectively. Similar thermal constants of 267.9DD (on the aphid diet) and 266.3DD (on the factitious food) were calculated for the total development of A. bipunctata, indicating the nutritional value of the factitious food

Graph-based process mining

Process mining is an area of research that supports discovering information about business processes from their execution event logs. The increasing amount of event logs in organizations challenges current process mining techniques, which tend to load data into the memory of a computer. This issue limits the organizations to apply process mining on a large scale and introduces risks due to the lack of data management capabilities. Therefore, this paper introduces and formalizes a new approach to store and retrieve event logs into/from graph databases. It defines an algorithm to compute Directly Follows Graph (DFG) inside the graph database, which shifts the heavy computation parts of process mining into the graph database. Calculating DFG in graph databases enables leveraging the graph databases' horizontal and vertical scaling capabilities in favor of applying process mining on a large scale. Besides, it removes the requirement to move data into analysts' computer. Thus, it enables using data management capabilities in graph databases. We implemented this approach in Neo4j and evaluated its performance compared with current techniques using a real log file. The result shows that our approach enables the calculation of DFG when the data is much bigger than the computational memory. It also shows better performance when dicing data into small chunks

Adversarial Lagrangian Integrated Contrastive Embedding for Limited Size Datasets

Certain datasets contain a limited number of samples with highly various styles and complex structures. This study presents a novel adversarial Lagrangian integrated contrastive embedding (ALICE) method for small-sized datasets. First, the accuracy improvement and training convergence of the proposed pre-trained adversarial transfer are shown on various subsets of datasets with few samples. Second, a novel adversarial integrated contrastive model using various augmentation techniques is investigated. The proposed structure considers the input samples with different appearances and generates a superior representation with adversarial transfer contrastive training. Finally, multi-objective augmented Lagrangian multipliers encourage the low-rank and sparsity of the presented adversarial contrastive embedding to adaptively estimate the coefficients of the regularizers automatically to the optimum weights. The sparsity constraint suppresses less representative elements in the feature space. The low-rank constraint eliminates trivial and redundant components and enables superior generalization. The performance of the proposed model is verified by conducting ablation studies by using benchmark datasets for scenarios with small data samples.Comment: Submitted to Neural Networks Journal: 36 pages, 6 figure