Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools of network science when the weight of edges are complex numbers. Here, we focus on the case when the weight matrix is Hermitian, a reasonable assumption in many applications, and investigate both structural and dynamical properties of the complex-weighted networks. Building on concepts from signed graphs, we introduce a classification of complex-weighted networks based on the notion of structural balance, and illustrate the shared spectral properties within each type. We then apply the results to characterise the dynamics of random walks on complex-weighted networks, where local consensus can be achieved asymptotically when the graph is structurally balanced, while global consensus will be obtained when it is strictly unbalanced. Finally, we explore potential applications of our findings by generalising the notion of cut, and propose an associated spectral clustering algorithm. We also provide further characteristics of the magnetic Laplacian, associating directed networks to complex-weighted ones. The performance of the algorithm is verified on both synthetic and real networks.

We are concerned with retrieving a query person from multiple videos captured by a non-overlapping camera network. Existing methods often rely on purely visual matching or consider temporal constraints but ignore the spatial information of the camera network. To address this issue, we propose a pedestrian retrieval framework based on cross-camera trajectory generation, which integrates both temporal and spatial information. To obtain pedestrian trajectories, we propose a novel cross-camera spatio-temporal model that integrates pedestrians' walking habits and the path layout between cameras to form a joint probability distribution. Such a spatio-temporal model among a camera network can be specified using sparsely sampled pedestrian data. Based on the spatio-temporal model, cross-camera trajectories can be extracted by the conditional random field model and further optimized by restricted non-negative matrix factorization. Finally, a trajectory re-ranking technique is proposed to improve the pedestrian retrieval results. To verify the effectiveness of our method, we construct the first cross-camera pedestrian trajectory dataset, the Person Trajectory Dataset, in real surveillance scenarios. Extensive experiments verify the effectiveness and robustness of the proposed method.

Normalized mutual information is widely used as a similarity measure for evaluating the performance of clustering and classification algorithms. In this paper, we show that results returned by the normalized mutual information are biased for two reasons: first, because they ignore the information content of the contingency table and, second, because their symmetric normalization introduces spurious dependence on algorithm output. We introduce a modified version of the mutual information that remedies both of these shortcomings. As a practical demonstration of the importance of using an unbiased measure, we perform extensive numerical tests on a basket of popular algorithms for network community detection and show that one's conclusions about which algorithm is best are significantly affected by the biases in the traditional mutual information.

Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

Computer simulations, especially of complex phenomena, can be expensive, requiring high-performance computing resources. Often, to understand a phenomenon, multiple simulations are run, each with a different set of simulation input parameters. These data are then used to create an interpolant, or surrogate, relating the simulation outputs to the corresponding inputs. When the inputs and outputs are scalars, a simple machine learning model can suffice. However, when the simulation outputs are vector valued, available at locations in two or three spatial dimensions, often with a temporal component, creating a surrogate is more challenging. In this report, we use a two-dimensional problem of a jet interacting with high explosives to understand how we can build high-quality surrogates. The characteristics of our data set are unique - the vector-valued outputs from each simulation are available at over two million spatial locations; each simulation is run for a relatively small number of time steps; the size of the computational domain varies with each simulation; and resource constraints limit the number of simulations we can run. We show how we analyze these extremely large data-sets, set the parameters for the algorithms used in the analysis, and use simple ways to improve the accuracy of the spatio-temporal surrogates without substantially increasing the number of simulations required.

Numerical association rule mining is a widely used variant of the association rule mining technique, and it has been extensively used in discovering patterns and relationships in numerical data. Initially, researchers and scientists integrated numerical attributes in association rule mining using various discretization approaches; however, over time, a plethora of alternative methods have emerged in this field. Unfortunately, the increase of alternative methods has resulted into a significant knowledge gap in understanding diverse techniques employed in numerical association rule mining -- this paper attempts to bridge this knowledge gap by conducting a comprehensive systematic literature review. We provide an in-depth study of diverse methods, algorithms, metrics, and datasets derived from 1,140 scholarly articles published from the inception of numerical association rule mining in the year 1996 to 2022. In compliance with the inclusion, exclusion, and quality evaluation criteria, 68 papers were chosen to be extensively evaluated. To the best of our knowledge, this systematic literature review is the first of its kind to provide an exhaustive analysis of the current literature and previous surveys on numerical association rule mining. The paper discusses important research issues, the current status, and future possibilities of numerical association rule mining. On the basis of this systematic review, the article also presents a novel discretization measure that contributes by providing a partitioning of numerical data that meets well human perception of partitions.

Unlike traditional unsupervised clustering, semi-supervised clustering allows users to provide meaningful structure to the data, which helps the clustering algorithm to match the user's intent. Existing approaches to semi-supervised clustering require a significant amount of feedback from an expert to improve the clusters. In this paper, we ask whether a large language model can amplify an expert's guidance to enable query-efficient, few-shot semi-supervised text clustering. We show that LLMs are surprisingly effective at improving clustering. We explore three stages where LLMs can be incorporated into clustering: before clustering (improving input features), during clustering (by providing constraints to the clusterer), and after clustering (using LLMs post-correction). We find incorporating LLMs in the first two stages can routinely provide significant improvements in cluster quality, and that LLMs enable a user to make trade-offs between cost and accuracy to produce desired clusters. We release our code and LLM prompts for the public to use.

The ability to design novel proteins with higher fitness on a given task would be revolutionary for many fields of medicine. However, brute-force search through the combinatorially large space of sequences is infeasible. Prior methods constrain search to a small mutational radius from a reference sequence, but such heuristics drastically limit the design space. Our work seeks to remove the restriction on mutational distance while enabling efficient exploration. We propose Gibbs sampling with Graph-based Smoothing (GGS) which iteratively applies Gibbs with gradients to propose advantageous mutations using graph-based smoothing to remove noisy gradients that lead to false positives. Our method is state-of-the-art in discovering high-fitness proteins with up to 8 mutations from the training set. We study the GFP and AAV design problems, ablations, and baselines to elucidate the results.

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. We demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

Dictionary learning is an effective tool for pattern recognition and classification of time series data. Among various dictionary learning techniques, the dynamic time warping (DTW) is commonly used for dealing with temporal delays, scaling, transformation, and many other kinds of temporal misalignments issues. However, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparseness coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparing with various benchmark methods.