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There are various issues of the K-Means Algorithm which are as follows −Handling Empty Clusters − The first issue with the basic K-means algorithm given prior is that null clusters can be acquired if no points are allocated to a cluster during the assignment phase. If this occurs, then a method is needed to choose a replacement centroid, because the squared error will be larger than necessary.One method is to select the point that is farthest away from some recent centroid. If this removes the point that currently contributes some total squared error. Another method is to select the replacement ... Read More
K-means clustering is the most common partitioning algorithm. K-means reassigns each data in the dataset to only one of the new clusters formed. A record or data point is assigned to the nearest cluster using a measure of distance or similarity.The k-means algorithm creates the input parameter, k, and division a group of n objects into k clusters so that the resulting intracluster similarity is large but the intercluster analogy is low. Cluster similarity is computed regarding the mean value of the objects in a cluster, which can be looked at as the cluster’s centroid or center of gravity.There are ... Read More
Cluster analysis is used to form groups or clusters of the same records depending on various measures made on these records. It can define the clusters in ways that can be beneficial for the objective of the analysis. This data has been used in several areas, such as astronomy, archaeology, medicine, chemistry, education, psychology, linguistics, and sociology.There are various types of clusters which are as follows −Well-Separated − A cluster is a group of objects in which every element is nearer to every other element in the cluster than to some object not in the cluster. Sometimes a threshold can ... Read More
There are various types of clustering which are as follows −Hierarchical vs Partitional − The perception between several types of clusterings is whether the set of clusters is nested or unnested, or in popular terminology, hierarchical or partitional. A partitional clustering is a distribution of the group of data objects into non-overlapping subsets (clusters) including every data object is in truly one subset.It can allow clusters to have subclusters, therefore it is required hierarchical clustering, which is a group of nested clusters that are assigned as a tree. Every node (cluster) in the tree (except for the leaf nodes) is ... Read More
The process of combining a set of physical or abstract objects into classes of the same objects is known as clustering. A cluster is a set of data objects that are the same as one another within the same cluster and are disparate from the objects in other clusters. A cluster of data objects can be considered collectively as one group in several applications. Cluster analysis is an essential human activity.Cluster analysis is used to form groups or clusters of the same records depending on various measures made on these records. The key design is to define the clusters in ... Read More
There are two approaches for determining the expected support of a pattern using (a concept hierarchy and a neighborhood-based approach called indirect association.Support Expectation Based on Concept HierarchyObjective measures alone cannot be adequate to remove uninteresting infrequent patterns. For instance, consider bread and laptop computer are frequent items. Even though the itemset {bread, Iaptop conputer} is infrequent and possibly negatively correlated, it is not fascinating because their lack of support appears clear to domain experts. Hence, a subjective approach for deciding expected support is required to prevent generating such infrequent patterns.Support Expectation Based on Indirect AssociationConsider a pair of items, ... Read More
The first class of techniques produced for mining infrequent patterns considers each item as a symmetric binary variable. The transaction information can be binarized by augmenting it with negative items. It displays an instance of changing the initial data into transactions having both positive and negative items. By using current frequent itemset generation algorithms including Apriori on the augmented transactions, some negative itemsets can be derived.Such an approach is possible only if several variables are considered as symmetric binary (i.e., it is viewed for negative patterns containing the negation of only a small number of items). If each item should ... Read More
In this problem, we are given two arrays arr[] and del[]. Our task is to find the smallest after deleting given elements.We will be deleting values from the array arr[] that are present in del[]. And then print the smallest value after deletion.Let’s take an example to understand the problem, Input arr[] = {2, 5, 6, 9, 1} del[] = {1, 5, 9}Output 2Solution ApproachA simple solution to the problem is using hashing. We will insert all the values of del[] array in the hash table. Then we will traverse the array arr[] and check if the values in the ... Read More
In this problem, we are given a number N. Our task is to find the slope of the given number.Slope of a number is the total number of maxima and minima digits in the number.Maxima digit is the digit whose both neighbours (previous and next) are smaller.Maxima digit is the digit whose both neighbours (previous and next) are greater.Let’s take an example to understand the problem, Input N = 9594459Output 2Solution ApproachA simple solution to the problem is by traversing the number digit by digit from excluding the first and last one (the don’t count form maxima or minima). Now, ... Read More
In this problem, we are given a number K. Our task is to find the Minimum Fibonacci terms with sum equal to K.Fibonacci Series generates subsequent numbers by adding two previous numbers. The Fibonacci series starts from two numbers − F0 & F1. The initial values of F0 & F1 can be taken 0, 1 or 1, 1 respectively.Fibonacci Series is 0 1 1 2 3 5 8 13Let’s take an example to understand the problem, InputK = 5Output2ExplanationThe sum 5 can be made using 3 and 2.Solution ApproachBy using Fibonacci numbers we can get the sum as any number ... Read More