Hierarchical Cluster Structure Research Articles

Chiral Solvent-Induced Homochiral Hierarchical Molecular Assemblies at the Liquid/Solid Interface.

We herein investigate the formation of homochiral hierarchical self-assembled molecular networks (SAMNs) via chirality induction by the coadsorption of a chiral solvent at the liquid/graphite interface by means of scanning tunneling microscopy (STM). In a mixture of achiral solvents, 1-hexanoic acid, and 1,2,4-trichlorobenzene, an achiral dehydrobenzo[12]annulene (DBA) derivative with three alkoxy and three hydroxy groups in an alternating manner forms chiral hierarchical triangular cluster structures through dynamic self-sorting. Enantiomorphous domains appear in equal probability. On the other hand, in chiral 2-methyl-1-hexanoic acid as a solvent, this molecule produces (i) homochiral small triangular clusters at a low solute concentration, (ii) a chirality-biased hierarchical structure consisting of triangular cluster structures with different cluster sizes at a medium concentration, and (iii) a dense structure with no chirality bias at a high concentration. We attribute the concentration-dependent degree of the chirality transmission to the number of coadsorbed solvent molecules in the SAMNs and to the difference in nucleus structure and size in the initial stage of the SAMN formation.

Leaf cluster morphology is altered along a local light gradient in different manners between young and old Fagus crenata crowns

ABSTRACT Leaf cluster morphological variation within and among Fagus crenata crowns was examined by analysing hierarchical leaf cluster structure. Leaf clusters were defined as a continuous group of leafy voxels, where each voxel was classified as part of a cluster if its effective leaf area density (eLAD) exceeded a threshold value. This threshold value ranged from sparse (10−1.3 m2 m−3) to dense (101.2 m2 m−3). Compared with young crowns, old crowns had a smaller effective leaf area index, a higher proportion of leafless space, more highly fragmented leaf clusters, and thinner clusters at all hierarchal levels, from smaller clusters with higher eLAD to large clusters with lower eLAD. Leaf clusters exhibited structural adaptability to the local light gradient within the crowns. For instance, we observed a positive correlation between leaf cluster thickness and inclination with relative light intensity. We hypothesized that the leaf cluster responses represented adaptations to changes in the light environment within crowns, particularly the increased light interception in lower crowns and the corresponding responses of leaves and twigs. However, cluster adaptation to local light conditions differed between young and old crowns. In young crowns, cluster thickness markedly varied with local light conditions, whereas cluster inclination did not respond. In old crowns, cluster inclination clearly adapted to local light conditions, whereas cluster thickness had little response.

Neurocognitive responses to spatial design behaviors and tools among interior architecture students: a pilot study

The impact of emotions on human behavior is substantial, and the ability to recognize people's feelings has a wide range of practical applications including education. Here, the methods and tools of education are being calibrated according to the data gained over electroencephalogram (EEG) signals. The issue of which design tools would be ideal in the future of interior architecture education, is an uncertain field. It is important to measure the students’ emotional states while using manual and digital design tools to determine the different impacts. Brain-computer interfaces have made it possible to monitor emotional states in a way that is both convenient and economical. In the research of emotion recognition, EEG signals have been employed, and the resulting literature explains basic emotions as well as complicated scenarios that are created from the combination of numerous basic emotions. The objective of this study is to investigate the emotional states and degrees of attachment experienced by interior architecture students while engaging in their design processes. This includes examining the use of 2D or 3D tools, whether manual or digital, and identifying any changes in design tool usage and behaviors that may be influenced by different teaching techniques. Accordingly, the hierarchical clustering which is a technique used in data analysis to group objects into a hierarchical structure of clusters based on their similarities has been conducted.

Typical and atypical solutions in nonconvex neural networks with discrete and continuous weights.

We study the binary and continuous negative-margin perceptrons as simple nonconvex neural network models learning random rules and associations. We analyze the geometry of the landscape of solutions in both models and find important similarities and differences. Both models exhibit subdominant minimizers which are extremely flat and wide. These minimizers coexist with a background of dominant solutions which are composed by an exponential number of algorithmically inaccessible small clusters for the binary case (the frozen 1-RSB phase) or a hierarchical structure of clusters of different sizes for the spherical case (the full RSB phase). In both cases, when a certain threshold in constraint density is crossed, the local entropy of the wide flat minima becomes nonmonotonic, indicating a breakup of the space of robust solutions into disconnected components. This has a strong impact on the behavior of algorithms in binary models, which cannot access the remaining isolated clusters. For the spherical case the behavior is different, since even beyond the disappearance of the wide flat minima the remaining solutions are shown to always be surrounded by a large number of other solutions at any distance, up to capacity. Indeed, we exhibit numerical evidence that algorithms seem to find solutions up to the SAT/UNSAT transition, that we compute here using an 1RSB approximation. For both models, the generalization performance as a learning device is shown to be greatly improved by the existence of wide flat minimizers even when trained in the highly underconstrained regime of very negative margins.

Internal tensile properties of characteristic zones in the electron beam weldment of TC17 titanium alloy

The internal tensile deformation of the individual base metal zone (BM), heat-affected zone (HAZ), and fusion zone (FZ) in a titanium alloy (Ti–5Al–2Sn–2r–4Mo–4Cr, wt.%) electron beam welding (EBW) joint is investigated. The ultimate strength of BM with a bimodal microstructure is 1047.5 MPa, and the elongation to fracture is 9.8%. HAZ is distinguished by the formation of a ghost structure with a hierarchical cluster structure within the initial αP grains, while the embedded αs laths dissolve in the matrix and relatively coarsening β grains are generated. During tension, the ghost structures strongly inhibit and deflect slip initiation and extension in the relatively coarsening β matrix. The competitive balance between strengthening from the ghost structure and weakening from the coarsening matrix dominates the mechanical properties of the HAZ, which then induces a hybrid fracture. The needle-shaped thermal martensite that formed during EBW causes the FZ to fail prematurely. The microstructural evolution of HAZ and FZ decreases their mechanical properties. This research may shed some light on the mechanical enhancement of titanium alloys by utilizing the multiple αL laths precipitated within the initial αP structure associated with the bimodal matrix.

Hierarchical co-clustering with augmented matrices from external domains

Co-clustering simultaneously classifies row and column objects of data matrices and is considered to have better accuracy than conventional one-way clustering methods. In the era of big data, extracting classification knowledge about objects from several domains has become increasingly feasible. This study proposes a hierarchical co-clustering with augmented matrices (HICCAM), which co-clusters the row and column objects of a target matrix while utilizing the augmented data matrices of these target objects extracted from the external domains. The algorithm is designed to improve classification accuracy by transferring knowledge in augmented matrices and simultaneously improves cluster interpretability using hierarchical cluster structures. Experiments on document clustering confirmed that HICCAM achieved the highest accuracy among comparison methods with and without external knowledge. Its clusters exhibit hierarchical relationships according to their topics. In addition, we provide the experimental results with multiview synthetic datasets that demonstrate a clustering situation in which HICCAM can be effectively identified.

Spatiotemporal studies of molecular clusters with neutron scattering methodology

Advanced neutron scattering techniques have the unique advantages of comprehensively characterizing the hierarchical structure and dynamic behavior of molecular clusters (MCs) at a wide range of spatial and temporal scales. Therefore, the application of neutron scattering techniques can provide spatiotemporal information of MCs concerned about both the structure and dynamics topics. This will help us to get insight into their structure-property relationships and guide the rational design of MCs-based functional materials applicable for diverse application scenarios.

FHC-NDS: Fuzzy Hierarchical Clustering of Multiple Nominal Data Streams

The need of fuzzy clustering arises in many real-world applications such as clumping the users based on their web browsing behavior where the behavior of a user can be similar to two different sets of users at the same instance. The aptness of fuzzy clustering for data streams is further intensified given their concept evolving nature. Data streams can be clustered either by following clustering-by-variable approach or clustering-by-example approach. Most of the existing fuzzy clustering-by-variable methods are applicable to numeric data streams only. In this article, a fuzzy hierarchical clustering method is proposed for clustering multiple nominal data streams using clustering-by-variable approach. The fuzzy affinity of data streams to different clusters is calculated using normalized cosine similarity to the cluster centroids. It handles the concept evolution by updating the hierarchical clustering structure by either merging and/or splitting the nodes depending on the extent to which the node entropy changes. The performance of the proposed method is analyzed and compared to hierarchical clustering for multiple nominal data streams (HCND), semifuzzy online divisive-agglomerative clustering, and nTreeClus on synthetic as well as real-world web-browsing dataset where it has outperformed all three in terms of cluster quality as quantified by Dunn index, modified Hubert <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Gamma$</tex-math></inline-formula> statistic, and adjusted rand index. Furthermore, the experimental results show that the proposed method is highly promising with regard to capturing fuzzy clusters as indicated by Xie-Beni index, partition coefficient, and partition entropy.

Super-resolved SIM imaging revealed hierarchical organization of the ryanodine receptor network in 3 dimensions in rabbit sinoatrial node cells.

The heartbeat is initiated by specialized sinoatrial node cells (SANCs). The rate of the heartbeat is regulated by Ca released from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) interacting with voltage and Ca-dependent membrane ion currents in SANCs. The released Ca takes the form of localized Ca releases (LCRs) that propagate for limited distances in wave-like manner. A computational model of SANCs, previously developed in our laboratory, simulates LCR synchronization mechanism as hierarchical clustering of surface RyRs based on confocal microscopy imaging data obtained in tangential sections of SANCs. The true detailed distribution of RyR clusters in 3D, however, remains unknown. Here, we applied a series of new computational approaches to experimental data obtained by super-resolved structured illumination microscopy in rabbit SANCs, in which RyRs were labeled by specific antibodies. Our approach consists of automated segmentation of RyR clusters with globally optimal detection and segmentation of objects with constant internal intensity distribution, followed by object-based colocalization analysis in 3D. Results are further refined with watershed transformations and computational geometry. Examinations of the images have revealed a hierarchical architecture of RyR network (positions and sizes of submembrane RyR clusters). After constructing a mathematical convex hull around the cell using RyR clusters as nodes, clusters were grouped based on their volume. The distribution of RyR clusters exhibited a wide range of sizes from 0.75 × 10−3 µm3 to 0.50 µm3 and cluster histograms followed a Poisson-like distribution. These new data have been incorporated in a new, realistic 3D model of SANC, in which heterogeneous RyR clusters facilitate LCR propagation. Impairment of the complex, hierarchical structure of RyR clusters may lead to sinus node dysfunction in aging and disease.

Hierarchical structure of YSO clusters in the W40 and Serpens South region: group extraction and comparison with fractal clusters

ABSTRACT Young stellar clusters are believed to inherit the spatial distribution like hierarchical structures of their natal molecular cloud during their formation. However, the change of the structures between the cloud and the young clusters is not well constrained observationally. We select the W40–Serpens South region (∼7 × 9 pc2) of the Aquila Rift as a testbed and investigate hierarchical properties of spatial distribution of young stellar objects (YSOs) in this region. We develop a minimum spanning tree (MST) based method to group stars into several levels by successively cutting down edges longer than an algorithmically determined critical value. A total of 832 YSOs are divided into 5 levels with 23 groups. For describing the hierarchical properties in a controlled way, we construct a set of synthetic source distributions at various fractal dimensions, and apply the same method to explore their group characters. By comparing the Q parameter and the surface density profiles of the observed and the synthetic data, we find that the YSO observation matches spatial patterns from multifractal dimensions. In the periphery region where the molecular clouds are more diffuse, the YSO structure is close to a fractal dimension of 2.0. While in the core regions, the fractal dimensions are close to 1.6 and 1.4 for the W40 and the Serpens South regions, respectively. Therefore, the YSOs may inherit the fractal pattern of the dense part of the molecular clouds, but such pattern dissipates slowly in several Myr.

A Multilevel Point Cloud Classification Method for Underground Tunnels Based on Three-Dimensional Moving LiDAR Measurements

Underground tunnel engineering requires complex systematic engineering. A tunnel requires internal measurements after the completion of shield construction to check the real construction quality of the tunnel and provide measurement data for the next tunnel project acceptance team. When measuring a tunnel’s internal construction and performing associated data analysis, it is necessary to accurately count the size and type information of the built tunnel internal structure. In this study, mobile three-dimensional laser scanning technology is used to collect a tunnel’s internal point cloud data, and many unordered point cloud data are collected. Thus, classifying the ground objects inside the tunnel automatically and accurately is a critical problem to be solved in a tunnel construction survey. Additionally, this study proposes a multilayer underground tunnel point cloud classification method that uses the hierarchical clustering structure to deal with the original tunnel point cloud. This method extracts the specific ground objects, such as tracks or roads, platforms, and pipelines, on the tunnel surface and inside the tunnel step by step. Concurrently, the accuracy of the projection plane and the accuracy of point cloud classification are introduced to evaluate the accuracy and finally calculate the statistics of ground object information in the tunnel. To verify the engineering practicability of this method, we first collected the point cloud data of a railway tunnel inside the tunnel using a rail car equipped with high-precision LiDAR and divided the data results into four sample areas for the classification test. To verify the algorithm’s robustness, we use the proposed method to test the highway tunnel data according to the same experimental process. Experiments show that this paper’s multilevel tunnel point cloud classification method can accurately extract these four types of ground objects. The average accuracy of the projection plane in each experimental area is not less than 91.49%, and the average accuracy of point cloud classification is not less than 92.63%. Compared with the other three types of classification methods in the same field, the method in this paper is more suitable for processing tunnel point cloud data and has the advantages of high classification accuracy, strong robustness, and a simple implementation process. The proposed method can also meet the real needs of underground tunnel internal construction surveys.

Network Extraction and Analysis of Character Relationships in Chinese Literary Works.

Character relationships in literary works can be interpreted and analyzed from the perspective of social networks. Analysis of intricate character relationships helps to better understand the internal logic of plot development and explore the significance of a literary work. This paper attempts to extract social networks from Chinese literary works based on co-word analysis. In order to analyze character relationships, both social network analysis and cluster analysis are carried out. Network analysis is performed by calculating degree distribution, clustering coefficient, shortest path length, centrality, etc. Cluster analysis is used for partitioning characters into groups. In addition, an improved visualization method of hierarchical clustering is proposed, which can clearly exhibit character relationships within clusters and the hierarchical structure of clusters. Finally, experimental results demonstrate that the proposed method succeeds in establishing a comprehensive framework for extracting networks and analyzing character relationships in Chinese literary works.

A Study on Performance Improvement of Intrusion Detection using Efficient Authentication and Distributed Monitoring

In a Mobile Ad hoc Network (MANET), mobile nodes play multiple roles as hosts and routers and are dynamically changing multi-hop structures. MANET consists only of wireless nodes with limit processing power, and routing and data transfer are performed through cooperation with each other. It is exposed to many attack threats due to the dynamic topology by the movement of the nodes and the characteristic of multi-hop communication. Therefore, in MANET, a technique that can detect effectively must be applied while detecting malicious nodes and reducing the impact of various attacks. In this paper, we propose an trust based authentication technique for nodes and a distributed monitoring technique to improve the detection performance of malicious nodes. The hierarchical cluster structure was used to improve authentication of nodes and detection performance and management efficiency of malicious nodes. A lightweight authentication technique of member nodes in the cluster was applied and the efficiency of node authentication was improved. It was used to determine whether it was an attack node by transmitting traffic monitoring information for neighbor nodes to CA and using. In addition, the efficient authentication technique using only key exchange without anyone's help was applied in order to provide integrity when exchanging information between cluster heads. Through this, it was possible to be free from trust information about nodes and forgery and falsification of information about attack nodes. The superiority of the technique proposed in this paper was confirmed through comparative experiments with the existing intrusion detection technique.

Density-Based Clustering of Social Networks

Abstract The idea of the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. The correspondence between clusters and dense regions in the sample space is here exploited to discuss an extension of this approach to the analysis of social networks. Conceptually, the notion of high-density cluster fits well the one of community in a network, regarded to as a collection of individuals with dense local ties in its neighbourhood. The lack of a probabilistic notion of density in networks is turned into a strength of the proposed method, where node-wise measures that quantify the role of actors are used to derive different community configurations. The approach allows for the identification of a hierarchical structure of clusters, which may catch different degrees of resolution of the clustering structure. This feature well fits the nature of social networks, disentangling different involvements of individuals in aggregations.

DendroMap: Visual Exploration of Large-Scale Image Datasets for Machine Learning with Treemaps.

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Energy‐efficient routing protocol and optimized passive clustering in WSN for SMART grid applications

SummaryDue to low cost, ease of implementation and flexibility of wireless sensor networks (WSNs), WSNs are considered to be an essential technology to support the smart grid (SG) application. The prime concern is to increase the lifetime in order to find the active sensor node and thereby to find once the sensor node (SN) dies in any region. For this reason, an energy‐efficient Dynamic Source Routing (DSR) protocol needs to provide the right stability region with a prolonged network lifetime. This work is an effort to extend the network's existence by finding and correcting the considerable energy leveraging behaviors of WSN. We build a comprehensive model based on real measures of SG path loss for different conditions by using the characteristics of WSN nodes and channel characteristics. This method also establishes a hierarchical network structure of balanced clusters and an energy‐harvesting SN. The cluster heads (CHs) are chosen by these SN using a low overhead passive clustering strategy. The cluster formation method is focused on the use of passive clustering of the particle swarm optimization (PSO). For the sake of eliminating delayed output in the WSN, energy competent dynamic source routing protocol (EC‐DSR) is used. Chicken swarm optimization (CSO) in which optimum cluster path calculation shall be done where distance and residual energy should be regarded as limitation. Finally, the results are carried out with regard to the packet distribution ratio, throughput, overhead management, and average end‐to‐end delay to demonstrate the efficiency of the proposed system.

Urban area and nature-based solution: Is this an attractive solution for Generation Z?

Finding solutions for the careful management of our natural heritage is fundamental to sustaining humanity on the planet. In this sense, nature-based solutions (NBS), which are useful initiatives aimed at addressing socio-environmental challenges to achieve a relatively more natural environment, can be a fundamental tool for reaching this goal in an urban context. However, there is no evidence that having NBS in urban cities could attract the young generations. The present study investigates Generation Z’s interest in NBS and explores the possibility of them considering a city that offers NBS as a possible tourism destination. This study uses different NBS initiatives implemented in the metropolitan area of Turin. Using quantitative approaches to qualitative responses, that is, multiple correspondence analysis and hierarchical cluster analysis, a hierarchical cluster structure was designed and gradually explored to identify main groups of respondents and subsequently deeper partitions. The results show that Generation Z perceives NBS initiatives as important for safeguarding and enhancing the cultural and natural heritage of the urban areas involved, which can improve their touristic and leisure value. This study is particularly relevant since it can help institutions to consider a new approach to stimulating proximity tourism in urban cities and their surroundings, by valorizing NBS as a possible attraction for Generation Z.

Data-driven effective model shows a liquid-like deep learning

The geometric structure of an optimization landscape is argued to be fundamentally important to support the success of deep neural network learning. A direct computation of the landscape beyond two layers is hard. Therefore, to capture the global view of the landscape, an interpretable model of the network-parameter (or weight) space must be established. However, the model is lacking so far. Furthermore, it remains unknown what the landscape looks like for deep networks of binary synapses, which plays a key role in robust and energy efficient neuromorphic computation. Here, we propose a statistical mechanics framework by directly building a least structured model of the high-dimensional weight space, considering realistic structured data, stochastic gradient descent training, and the computational depth of neural networks. We also consider whether the number of network parameters outnumbers the number of supplied training data, namely, over- or under-parametrization. Our least structured model reveals that the weight spaces of the under-parametrization and over-parameterization cases belong to the same class, in the sense that these weight spaces are well-connected without any hierarchical clustering structure. In contrast, the shallow-network has a broken weight space, characterized by a discontinuous phase transition, thereby clarifying the benefit of depth in deep learning from the angle of high dimensional geometry. Our effective model also reveals that inside a deep network, there exists a liquid-like central part of the architecture in the sense that the weights in this part behave as randomly as possible, providing algorithmic implications. Our data-driven model thus provides a statistical mechanics insight about why deep learning is unreasonably effective in terms of the high-dimensional weight space, and how deep networks are different from shallow ones.

Enhancing Obstructive Sleep Apnea Diagnosis With Screening Through Disease Phenotypes: Algorithm Development and Validation

BackgroundThe American Academy of Sleep Medicine guidelines suggest that clinical prediction algorithms can be used in patients with obstructive sleep apnea (OSA) without replacing polysomnography, which is the gold standard.ObjectiveThis study aims to develop a clinical decision support system for OSA diagnosis according to its standard definition (apnea-hypopnea index plus symptoms), identifying individuals with high pretest probability based on risk and diagnostic factors.MethodsA total of 47 predictive variables were extracted from a cohort of patients who underwent polysomnography. A total of 14 variables that were univariately significant were then used to compute the distance between patients with OSA, defining a hierarchical clustering structure from which patient phenotypes were derived and described. Affinity from individuals at risk of OSA phenotypes was later computed, and cluster membership was used as an additional predictor in a Bayesian network classifier (model B).ResultsA total of 318 patients at risk were included, of whom 207 (65.1%) individuals were diagnosed with OSA (111, 53.6% with mild; 50, 24.2% with moderate; and 46, 22.2% with severe). On the basis of predictive variables, 3 phenotypes were defined (74/207, 35.7% low; 104/207, 50.2% medium; and 29/207, 14.1% high), with an increasing prevalence of symptoms and comorbidities, the latter describing older and obese patients, and a substantial increase in some comorbidities, suggesting their beneficial use as combined predictors (median apnea-hypopnea indices of 10, 14, and 31, respectively). Cross-validation results demonstrated that the inclusion of OSA phenotypes as an adjusting predictor in a Bayesian classifier improved screening specificity (26%, 95% CI 24-29, to 38%, 95% CI 35-40) while maintaining a high sensitivity (93%, 95% CI 91-95), with model B doubling the diagnostic model effectiveness (diagnostic odds ratio of 8.14).ConclusionsDefined OSA phenotypes are a sensitive tool that enhances our understanding of the disease and allows the derivation of a predictive algorithm that can clearly outperform symptom-based guideline recommendations as a rule-out approach for screening.

Multi-dimensional analysis of regional investment attractiveness in Poland

Research background: A given region's investment attractiveness is a set of conditions that depend primarily on the policy of the country that is the recipient of direct foreign investment, encouraging or discouraging foreign investors from making decisions about locating investments in a given area. These conditions include the economic conditions, the infrastructure, the political and legal system, the business environment, and the sociocultural environment. a foreign investor, the motive for exporting capital abroad is the search for benefits that can be derived from the business activity conducted there, including easier entry into new markets. Purpose of the article: The main aim of the paper is to distinguish groups of voivodeships (NUTS 2 level) that are relatively homogeneous in terms of investment attractiveness, which is conducive to the inflow of foreign capital and the implementation of investment projects involving foreign capital. Methods: Distinguishing groups of voivodeships similar to each other in terms of the level of investment attractiveness is made by applying hierarchical cluster analysis. The dendrogram illustrates the hierarchical structure of clusters of similar objects according to the analysed set of variables. The quality of the clustering result is also assessed by determining the silhouette index. Comparative and descriptive analysis of CSO statistics are additional methods used that have contributed to the achievement of the aim of the paper. The research period covers the years 2000?2018. Findings &amp; value added: The investment attractiveness of a voivodeship is closely related to the level of its economic development. Therefore, the following voivodeships are listed at the top of the investment attractiveness rankings: Mazowieckie, Dolnośląskie, Śląskie, Małopolskie, and Pomorskie. The conducted study has confirmed that the creation of special economic zones and the development of regional smart specialisations contribute to the inflow of foreign capital. It is worth noting that the assessment of investment attractiveness is relative. The comparison of the innovative attractiveness of voivodeships is based on the use of the average value, overestimated by cities, i.e. central hubs, attracting investors. The regional perspective on investment attractiveness using multi-dimensional statistical analysis methods is the added value of the article.