Pavel Prazak

The projected clustering (PROCLUS) algorithm is a subspace clustering algorithm based on the k-medoids clustering approach. It is designed to address the challenges of irrelevant received signal strength (RSS) measurements in fingerprint vectors by focusing on meaningful subsets of RSS measurements from wireless APs, known as subspaces. Despite its robustness, its performance heavily depends on the chosen similarity metric, with Euclidean and Manhattan distances being the most common. While many researchers focus on modifying the algorithm to enhance performance, the impact of similarity metrics on clustering performance is often overlooked, despite its critical role in determining accuracy. As such, this paper evaluates the clustering performance of the PROCLUS algorithm using five distance-based similarity metrics—Euclidean, Manhattan, Cosine similarity, Canberra, and Chebyshev—across six experimentally generated fingerprint databases. It aims to identify the best similarity metric for maximizing clustering performance for each of the six fingerprint databases, with silhouette scores used as the clustering performance metric. Simulation results show that Cosine similarity is the most effective metric with the PROCLUS algorithm. It consistently produces clusters with the highest silhouette scores, all well above the 0.25 threshold and were 24% to 136% higher than the scores achieved using the other distance-based metrics across the tested fingerprint databases. The Canberra distance performed variably, while Euclidean and Manhattan distances were less reliable. The Chebyshev distance consistently underperformed in all the databases considered. The findings in this paper highlight the importance of choosing the appropriate similarity metric to perform clustering operations with the PROCLUS algorithm.

A manager's key task is to find the optimal solution, which can be difficult without advanced methods, data analysis or strategy evaluation. Game theory can help as a tool for decision making and achieving win-win outcomes in conflicts. Nash equilibrium applies to pure strategies, while matrix games without a saddle point require mixed strategies and linear programming. Given sufficient data, market competition can be modelled as a matrix game. This paper presents practical examples of the use of matrix games with linear programming in management. In particular, the paper deals with the following two decision problems: the conflict situation between two banks and the conflict situation between the company management and the trade union. Each case includes a formal description of the problem, the search for the optimal solution and the interpretation of the result from an economic point of view.

The correlation-based context similarity coefficient (CSC) metric is a pattern-based fingerprint similarity metric that has gained interest in fingerprint database clustering operations. The performance of the traditional distance-based metric in fingerprint vector similarity determination has been known to be influenced by the size of the fingerprint vector. However, as for the correlation-based CSC metric, there is no comprehensive research on how fingerprint vector size affects its performance in similarity determination and subsequently clustering performance. As such, this paper examines the impact of fingerprint vector size on the similarity determination performance of the correlation-based CSC metric with the k-medoids algorithm employed for clustering. The analysis is performed across four synthetic and two experimentally generated fingerprint databases with varying fingerprint vector sizes. The impact analysis is carried out with the clustering algorithm set to generate K ∈ [3, 5] clusters. Additionally, the results are compared against three distance-based metrics: squared Euclidean, Manhattan, and cosine. With silhouette score as the clustering performance metric, the simulation result shows that the size of the fingerprint vector influences the similarity determination performance of the correlation-based CSC metric. Additionally, the number of clusters in which the clustering algorithm is set to generate also contributes to how the correlation-based CSC metric performs in similarity determination. The similarity determination time complexity of the correlation-based CSC metric increases with fingerprint vector size, making efficient clustering more challenging as fingerprint vector sizes increase. For optimal performance, the correlation-based CSC metric is recommended for us as a similarity metric on a database with a fingerprint vector size of N ≤ 4 and a clustering algorithm configured to generate no more than 3 clusters.

Doi: 10.28991/HIJ-2025-06-01-022 Full Text: PDF

Fingerprint database clustering and localization using k‐medoids and k‐nearest neighbour (k‐NN) algorithms respectively typically use distance‐based fingerprint similarity metrics, with their performances dependent on the type of distance metric used. This paper proposes employing a pattern‐based metric, the context similarity coefficient (CSC), for both algorithms instead of traditional distance‐based metrics. The CSC accounts for fingerprint behaviour and the non‐linear relationships among fingerprints during the similarity measurement. The performance of both algorithms with the CSC as the similarity metric is evaluated on four publicly available fingerprint databases, using position root mean square error (RMSE) and silhouette score as performance metrics. These results are compared to those of the same algorithms using five distance‐based metrics: Euclidean, square Euclidean, Manhattan, cosine, and Chebyshev distances. The k‐medoids algorithm with CSC shows moderate clustering performance compared to the five distance‐based metrics considered. However, when combined with the k‐NN algorithm also using CSC, it achieves the highest localization accuracy, with at least a 29% improvement in position RMSE across all four databases. The results indicate that while k‐medoids with CSC may not create well‐separated clusters, combining it with the k‐NN algorithm with CSC as its similarity metric significantly enhances localization accuracy compared to distance‐based metrics.

The affinity propagation clustering (APC) algorithm is popular for fingerprint database clustering because it can cluster without pre-defining the number of clusters. However, the clustering performance of the APC algorithm heavily depends on the chosen fingerprint similarity metric, with distance-based metrics being the most commonly used. Despite its popularity, the APC algorithm lacks comprehensive research on how distance-based metrics affect clustering performance. This emphasizes the need for a better understanding of how these metrics influence its clustering performance, particularly in fingerprint databases. This paper investigates the impact of various distance-based fingerprint similarity metrics on the clustering performance of the APC algorithm. It identifies the best fingerprint similarity metric for optimal clustering performance for a given fingerprint database. The analysis is conducted across five experimentally generated online fingerprint databases, utilizing seven distance-based metrics: Euclidean, squared Euclidean, Manhattan, Spearman, cosine, Canberra, and Chebyshev distances. Using the silhouette score as the performance metric, the simulation results indicate that structural characteristics of the fingerprint database, such as the distribution of fingerprint vectors, play a key role in selecting the best fingerprint similarity metric. However, Euclidean and Manhattan distances are generally the preferable choices for use as fingerprint similarity metrics for the APC algorithm across most fingerprint databases, regardless of their structural characteristics. It is recommended that other factors, such as computational intensity and the presence or absence of outliers, be considered alongside the structural characteristics of the fingerprint database when choosing the appropriate fingerprint similarity metric for maximum clustering performance.

In fingerprint-based localization systems, clustering fingerprint databases is a proposed technique for improving localization accuracy while reducing localization time. Among various clustering algorithms, density-based spatial clustering of applications with noise (DBSCAN) stands out for its robustness to outliers and ability to accommodate fingerprint databases of various shapes. However, the clustering performance of the DBSCAN algorithm is heavily influenced by the type of similarity measure metric used, with most researchers using distance-based metrics. This paper aims to enhance DBSCAN clustering by using a pattern-based metric known as the context similarity coefficient (CSC) instead of distance-based metrics. The CSC metric examines received signal strength (RSS) measurement patterns that form fingerprint vectors and assesses both linear and non-linear relationships between these vectors to determine similarity. Four publicly available fingerprint databases were used to evaluate the clustering performance with silhouette scores as a performance metric. The performance of the DBSCAN algorithm with the CSC metric is determined and compared to Euclidean and Manhattan distances as similarity measure metrics. Simulation results indicate that achieving good clustering performance with the DBSCAN algorithm requires generating three or fewer clusters. The proposed CSC metric demonstrated the best clustering performance in two of four fingerprint databases and the second-best in another. However, computational complexity comparisons reveal that the CSC metric is highly computationally intensive and is suggested to be used on small to medium-sized fingerprint databases generated using an odd number of wireless APs deployed in a non-uniform or non-grid-like distribution.

Distance-based metrics are the most common fingerprint similarity metrics used in fingerprint database clustering and localization processes in a fingerprint-based localization system. In this paper, however, a less common but promising pattern-based fingerprint similarity metric is proposed as an alternative to the distance-base metric. The proposed fingerprint similarity metric is based on an inverse weight (IW) normalization of the context similarity coefficient (CSC)-based similarity metric measure. The clustering and localization performance of the fingerprint-based localization system with the proposed IW-CSC-based fingerprint similarity metric is determined and compared to the square Euclidean, Manhattan, and cosine distance-based metrics. The k-means algorithm with a k-means++ cluster initialization process is considered for fingerprint database clustering, while the k-nearest neighbor (k-NN) algorithm is considered for localization. Based on the four fingerprint databases considered, the proposed IW-CSC-based metric has the slowest localization time with moderate clustering performance. However, it has the best localization performance, which is at least 52% higher than the localization performances of the three distance-base metrics considered. The proposed IW-CSC-based metric is recommended as an alternative to the distance-base metric only when improved localization performance is the primary objective of the fingerprint-based localization system. It is also recommended for use in small to medium-sized fingerprint databases for clustering and localization.

Digital storytelling (DST) is one of the alternative teaching methods and previous research shows its positive impact on students’ motivation and learning outcomes, especially in humanities subjects. In vocational subjects such as economics, the effectiveness of this method is questionable. 856 respondents aged 15 to 19 from six business academies in the Czech Republic took part in the testing, which focused on the effectiveness of digital storytelling in economics. This paper presents other possible factors that may have influenced students' performance in the post-test. A comparison of the results from the pre-tests and post-tests of the experimental and control groups showed that the students from the experimental group reached higher mean values in the post-test than the students from the control group. It was also found that in the group that used digital storytelling, the year of study and the initial knowledge of the students assessed in the pre-test influenced the mean post-test scores. On the other hand, the factor of students' gender was not demonstrated. At the end of the testing, a questionnaire survey was conducted to investigate students' views on digital storytelling and their preferences for teaching methods.