A Comparative Study of Different Distances for Similarity Estimation

The security and integrity of computer systems and networks highly depend on malware detection. In the realm of malware detection, the K-Nearest Neighbors (KNN) algorithm is a well-liked and successful machine learning algorithm. However, the choice of an acceptable distance metric parameter has a significant impact on the KNN algorithm's performance. This study tries to improve malware detection by adjusting the KNN algorithm's distance metric parameter. The distance metric greatly influences the similarity or dissimilarity between instances in the feature space. The KNN algorithm for malware detection can be more accurate and effective by carefully choosing or modifying the distance metric. This paper analyzes multiple distance metrics, including Minkowski distance, Manhattan distance, and Euclidean distance. These metrics account for the traits of malware samples while capturing various aspects of similarity. The effectiveness of the KNN algorithm is evaluated using the MalMem-2022 malware dataset, and the results are broken down into these three-distance metrics. The experimental findings show that, among the three distance metric parameters, the Euclidean and Minkowski distance metric parameters considerably produced the best outcomes with binary classification. While with multiclass classification, the KNN algorithm has achieved the highest outcomes using Manhattan distance.

Content Based Image Retrieval (CBIR) is a process in which for a given query image similar images will be retrieved based on the image content similarity. Image content refers to its visual features, which are mathematical representations of a digital image. The image retrieval task primarily depends on image feature extraction and similarity measurement between the feature vectors. The performance of CBIR process not only decided by the optimum features extracted from the image but also on the proper choice of the similarity/dissimilarity measures (distance metrics). As the image features broadly diversified in terms of color, texture and shape based, using the same distance metric may not work well for all of these features. In this paper, first we presented overview of geometric and statistical distance metrics used in CBIR along with the comparative analysis of these measures on color and texture features. Color features extracted by computing color histograms in HSV space and texture features by wavelet decompositions. Geometrical distances such as Manhattan, Chebyshev, Euclidean, statistical distance metrics such as Cosine Similarity, Chi-square, KullbackLeibler, Jeffrey and cumulative statistical distance metrics of Kolmogorov-Smirnov, Cramer von Mises and Earthmover's distances were analyzed for feature similarity. We gave certain conclusions on the performance of all these distance metrics in terms of Mean Average Precision (MAP) and Recall rates with color and texture features respectively.

Data mining is a collection of methods used to extract useful information from large data bases. Cluster Analysis refers to the grouping of a set of data points into clusters. Most widely used partitioning methods are K-means and Fuzzy c-means (FCM) algorithms. However, they suffer from the difficulties such as random selection of initial centre values and handling outlier data points. Most of the existing clustering methods use the Euclidean distance metric. The modified fuzzy c-means algorithm (MFCM) is efficient in handling outlier data points. In this paper, a new hybrid algorithm is proposed to solve the limitations of the traditional clustering methods. The hybrid K-MFCM algorithm is tested on four real world bench mark data sets from UCI machine learning repository with various distance metrics including Euclidean, City Block and Chessboard. The cluster centroid values of hybrid algorithm are calculated for various data sets. The experimental results show that the hybrid algorithm gives good results in terms of objective function value and better fuzzy cluster validity results for chessboard distance metric than other distance metrics.

Instance-based learning techniques use a set of stored training instances to classify new examples. The most common such learning technique is the nearest neighbor method, in which new instances are classified according to the closest training instance. A critical element of any such method is the metric used to determine distance between instances. Euclidean distance is by far the most commonly used metric; no one, however, has systematically considered whether a different metric, such as Manhattan distance, might perform equally well on naturally occurring data sets. Some evidence from psychological research indicates that Manhattan distance might be preferable in some circumstances. This paper examines three different distance metrics and presents experimental comparisons using data from three domains: malignant cancer classification, heart disease diagnosis, and diabetes prediction. The results of these studies indicate that the Manhattan distance metric works works quite well, although not better than the Euclidean metric that has become a standard for machine learning experiments. Because the nearest neighbor technique provides a good benchmark for comparisons with other learning algorithms, the results below include a number of such comparisons, which show that nearest neighbor, using any distance metric, compares quite well to other machine learning techniques.

This paper represents a new approach for face recognition that incorporates Prewitt edge detection, Gabor filter and Zernike moments to transform the image into a unified domain. On this joint domain, five distance metrics are constructed using Schoenberg transform for the purpose of defining efficient similarity measures for holistic face recognition. The proposed Schoenberg similarity applies Schoenberg transform to the logarithm of five existing distance metrics: Minkowski, City-Block, Euclidean, Soergel and Lorentzian metrics. The constructed Schoenberg logarithmic metrics are called SL-Minkowski, SL-City-Block, SL-Euclidean, SL-Soergel and SL-Lorentzian. These distance metrics are utilized as similarity measures after being normalized over the range [0,1] for fair comparison with existing measures. The proposed Schoenberg system can resist three problems: Change in illumination, pose and facial expression. Simulation results show that the proposed distance measures have superior performance as compared to the classical metrics: Structural Similarity Index Measure (SSIM) and Feature-based Similarity Measure (FSIM). Performance criteria are the recognition rate and the recognition confidence, defined as the similarity difference between the best match and the second-best match in the face database.

This paper shows that a choice of weights in the fuzzy c-means algorithm affect the performance of a room equalizer. The ordinary fuzzy c-means (FCM) algorithm already proves useful to deriving an equalizing filter for multiple listeners. A room impulse response models the behaviour of the sounds reflection in the room at each listener location. The FCM algorithm finds similar room impulse responses based on Euclidean distances among the impulse responses and groups them together. But the Euclidean distance used in the FCM implies equal weights for all parts of sound reverberation or reflection. The paper proposes an algorithm to obtain a room acoustic equalization filter based on weighted fuzzy c-means (WFCM) algorithm. The use of WFCM can give clustering more flexibility in obtaining a prototype for each cluster. Then combining the prototypes to obtain a representative room response that derives the inverse filter will be more effective. We use spectral deviation to measure how well each equalizing filter works. Experiments show that different weights in the WFCM algorithm can enhance or degrade the performance of the equalizing filter.

Clustering is a data mining method that is widely used to group data based on similarity. This clustering process can be used to streamline data so as to facilitate the data ranking process. The purpose of this study was to make comparisons of distance measurements on the K-Means and TOPSIS methods to select students who would take part in industrial visit activities. The method used in this study is the K-Means Algorithm to carry out the clustering process whose results will be processed using the TOPSIS method, both of which use Euclidean, Manhattan and Minkowsky Distance. Based on the clustering process, there were 21 respondents who were eligible to be included, then with TOPSIS a ranking process was carried out. Of the three distance measurements used based on the Pearson Euclidean distance correlation test, the highest results were 0.992, Manhattan 0.982 and Minkowsky 0.980, with ratings one, two and three respectively. For the Spearman correlation, Eculidean is 0.972, Manhattan is 0.982 and Minkowski is 0.955. Thus, Euclidean distance gives the best correlation results, while for alternatives, Manhattan distance or Minkoesky distance can be used.

Semantic similarity, the task of determining whether two sentences convey the same meaning, is central to applications such as paraphrase detection, semantic search, and question answering. Despite the widespread adoption of transformer-based models for this task, their performance is influenced by both the choice of similarity measure and BERT (bert-base-nli-mean-tokens), RoBERTa (all-roberta-large-v1), and MPNet (all-mpnet-base-v2) on the Microsoft Research Paraphrase Corpus (MRPC). Sentence embeddings were compared using cosine similarity, dot product, Manhattan distance, and Euclidean distance, with thresholds optimized for accuracy, balanced accuracy, and F1-score. Results indicate a consistent advantage for MPNet, which achieved the highest accuracy (75.6%), balanced accuracy (71.0%), and F1-score (0.836) when paired with cosine similarity at an optimized threshold of 0.671. BERT and RoBERTa performed competitively but exhibited greater sensitivity to the choice of Similarity metric, with BERT notably underperforming when using cosine similarity compared to Manhattan or Euclidean distance. Optimal thresholds varied widely (0.334–0.867), underscoring the difficulty of establishing a single, generalizable cut-off for paraphrase classification. These findings highlight the value of fine-tuning of both Similarity metrics and thresholds alongside model selection, offering practical guidance for designing high-accuracy semantic similarity systems in real-world NLP applications.

Multi-modal registration, especially CT/MR to ultrasound (US), is still a challenge, as conventional similarity metrics such as mutual information do not match the imaging characteristics of ultrasound. The main motivation for this work is to investigate whether a deep learning network can be used to directly estimate the displacement between a pair of multi-modal image patches, without explicitly performing similarity metric and optimizer, the two main components in a registration framework. The proposed DVNet is a fully convolutional neural network and is trained using a large set of artificially generated displacement vectors (DVs). The DVNet was evaluated on mono- and simulated multi-modal data, as well as real CT and US liver slices (selected from 3D volumes). The results show that the DVNet is quite robust on the single- and multi-modal (simulated) data, but does not work yet on the real CT and US images.

Data mining is a process which discovers patterns and retrieval knowledge in large datasets. Many learning and data mining algorithms rely on distance metrics. Cluster analysis is one of learning algorithms which adopted to biological data, for example, Microarray expression data. In this study, we assessed the validity of five distance metrics (Euclidean, Manhattan, Minkowski, Cosine and Mahalanobis) with the partitioning around medoids (PAM) algorithm on microarray datasets. Microarray datasets were pre-processed prior to analysis, and the evaluation of the algorithm was undertaken using Krzanowski-Lai validity index. Our results showed When selected microarray datasets were clustered with partitioning around medoids based on Manhattan distance, Minkowski, Cosine and Euclidean distance for different k partitions all exhibited unsatisfactory performance, however, the partitioning around medoids algorithm generates an optimal cluster solution when used with Mahalanobis distance.

The Recognition and Classification of Objects Based on the Modified Distance Metric

Fuzzy c-means (FCM) algorithms have been shown effective for image segmentation. A series of enhanced FCM algorithms incorporating spatial information have been developed for reducing the effect of noises. This paper presents a robust FCM algorithm with non-local spatial information for image segmentation, termed as NLFCM. It incorporates two factors: one is the local similarity measure depending on the differences between the central pixel and its neighboring pixels in the image; the other is the non-local similarity measure depended on all pixels whose neighborhood configurations are similar to their neighborhood pixels. Furthermore, an adaptive weight is introduced to control the trade-off between local similarity measure and non-local similarity measure. The experimental results on synthetic images and real images under different types of noises show that the new algorithm is effective, and they are relatively independent to the types of noises.

Data sparsity remains to be a critical concern for recommendation systems since it results in low accuracy and poor recommendation quality. To address this problem, collaborative filtering techniques based on user similarity have been applied but existing implementations have not been shown to sufficiently address the problem of data sparsity. Thus, this paper presents an enhanced memory-based collaborative filtering algorithm utilizing a new similarity measure that identifies co-rated items and computes user similarity to overcome the data sparsity problem and improve the recommendation quality which can be adopted for various applications. Results of the study show that the use of the new similarity measure has improved the determination of user similarity than when using the traditional Cosine, Euclidean Distance, and Pearson Correlation similarity metrics.

There has been a profound expansion of digital data both in terms of quality and heterogeneity. Trivial searching techniques of images by using metadata, keywords or tags are not sufficient. Efficient Content-based Image Retrieval (CBIR) is certainly the only solution to this problem. Difference between colors of two images can be an important metric to measure their similarity or dissimilarity. Content-based Image Retrieval is all about generating signatures of images in database and comparing the signature of the query image with these stored signatures. Color histogram can be used as signature of an image and used to compare two images based on certain distance metric.In this study, COREL Database is used for an exhaustive study of various distance metrics on different color spaces. Euclidean distance, Manhattan distance, Histogram Intersection and Vector Cosine Angle distances are used to compare histograms in both RGB and HSV color spaces. So, a total of 8 distance metrics for comparison of images for the sake of CBIR are discussed in this work.

The machine learning algorithms can be applied in many classification problems including the clinical studies. In the stroke emotion analysis, the machine learning is used to analyze the emotion of stroke patients and normal people. The K-Nearest Neighbor (KNN) classifier relies on the distance metric to calculate the nearest class for classification. The aim of this study is to compare the performances of different distance metrics apply on the classification of emotional electroencephalogram (EEG) between stroke and normal people. The Detrended Fluctuation Analysis (DFA) feature was extracted from the EEG signal of both classes and KNN was applied with different distance metrics for comparison. The results showed that the City Block distance metric performs the best among all. Moreover, the lower values of nearest neighbor were required to provide high classification result. The results from this study showed that the performance of the KNN classification was affected by the distance metric used.