is meth xwhy-this-method-will-not-only-speed-up-the-convergence-of-the-k-means-algorithm-but-also-gua/a26f943d-Search for textbooks, step-by-step explanations to homework questions, ..E AskFor the k-means algorithm, it is interesting tonote that by choosing the initial cluster centerscarefully,we may be able to not only speed up theconvergence of the algorithm, but alsoguarantee the qualityof the final clustering. The k-means++algorithm is a variant of k-means, whichchooses the initialers as follows. Firmly at random ftively, for each obsen center, it chooer. Thisct is chosen at raortional to dist(p) Iteratively, for each object p other than theancenp) to the closestn chosen. The itercers arected.lain why this methconvergence of thComputer Sccenters as follows. First, it selects one centeruniformly at random from the objects in the dataigArchitectureset.chosen center, it chooses an object as the newnguage Processingcenter. ThisearningDistribuobject is chosen at random with probabilityproportional to dist(p)2, where dist(p)) is thedistancetelligenceCompfrom p) to the closest center that has alreadybeen chosen. The iteration continues until kAlgorithmsrantee the qualityultscenters areselected.Explain why this methąd will not only speed upthe convergence of the k-means algorithm, butalsoguarantee the quality of the final clusteringresultso 9:15werPOFred

Kmeans algorithm is an iterative algorithm that tries to partition the dataset into Kpre-defined…

For the k-means algorithm, it is interesting to note that by choosing the initial cluster centers carefully, we may be able to not only speed up the convergence of the algorithm, but also quarantee the quality

For the k-means algorithm, it is interesting to note that by choosing the initial cluster centers carefully, we may be able to not only speed up the convergence of the algorithm, but also quarantee the quality

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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For the k-means algorithm, it is interesting to note that by choosing the initial cluster centers carefully, we may be able to not only speed up the convergence of the algorithm, but also guarantee the quality of the final clustering. The k-means++ algorithm is a variant of k-means, which chooses the initial centers as follows. First, it selects one center uniformly at random from the objects in the data set. Iteratively, for each object p other than the chosen center, it chooses an object as the new center. This object is chosen at random with probability proportional to dist(p)2, where dist(p)) is the distance from p) to the closest center that has already been chosen. The iteration continues until k centers are selected. Explain why this method will not only speed up the convergence of the k-means algorithm, but also guarantee the quality of the final clustering results jo 9:15
Correct answer will be upvoted else downvoted. Computer science. Presently you get Baby Ehab's first words: "Given an integer n, track down the longest aftereffect of [1,2,… ,n−1] whose item is 1 modulo n." Please take care of the issue. A succession b is an aftereffect of a cluster an if b can be gotten from a by erasing a few (conceivably all) components. The result of an unfilled aftereffect is equivalent to 1. Input The main line contains the integer n (2≤n≤105). Output The primary line ought to contain a solitary integer, the length of the longest aftereffect. The subsequent line ought to contain the components of the aftereffect, in expanding request. In case there are numerous arrangements, you can print any
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Andrey thinks he is genuinely a fruitful engineer, yet as a general rule he didn't know about the double inquiry calculation up to this point. Subsequent to perusing some writing Andrey comprehended that this calculation permits to rapidly find a specific number x in a cluster. that the components of the cluster are listed from nothing, and the division is done in integers (adjusting down). Andrey read that the calculation possibly works if the cluster is arranged. Notwithstanding, he tracked down this assertion false, in light of the fact that there unquestionably exist unsorted clusters for which the calculation track down x! Andrey needs to compose a letter to the book writers, yet prior to doing that he should consider the stages of size n to such an extent that the calculation tracks down x in them. A change of size n is an exhibit comprising of n unmistakable integers…
bob chose to give Tina gift. bob has as of now purchased a cluster an of length n yet, giving a cluster is excessively normal. Rather than that, he chose to gift Mila the portions of that cluster! bob needs his gift to be wonderful, so he chose to pick k non-covering sections of the exhibit [1,r1], [12,r2], ... [Ik,rk] to such an extent that: the length of the primary fragment [1,r1] is k, the length of the second portion [12,r2] is k-1, . , the length of the k-th section [Ik,rk] is 1 for each i
Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given one integer n (n>1). Review that a change of length n is a cluster comprising of n unmistakable integers from 1 to n in discretionary request. For instance, [2,3,1,5,4] is a change of length 5, yet [1,2,2] isn't a stage (2 shows up twice in the exhibit) and [1,3,4] is additionally not a change (n=3 but rather there is 4 in the cluster). Your undertaking is to track down a stage p of length n that there is no file I (1≤i≤n) to such an extent that pi=i (along these lines, for all I from 1 to n the condition pi≠i ought to be fulfilled). You need to answer t autonomous experiments. In case there are a few replies, you can print any. It tends to be demonstrated that the appropriate response exists for each n>1. Input The main line of the input contains one integer t (1≤t≤100) — the number of experiments. Then, at that point, t experiments follow. The main line of the experiment…
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You are given a cluster an of length 2n. Consider a segment of exhibit an into two aftereffects p and q of length n each (every component of cluster an ought to be in precisely one aftereffect: either in p or in q). We should sort p in non-diminishing request, and q in non-expanding request, we can indicate the arranged adaptations by x and y, individually. Then, at that point, the expense of a segment is characterized as f(p,q)=∑ni=1|xi−yi|. Track down the amount of f(p,q) over all right parcels of cluster a. Since the appropriate response may be too huge, print its remaining portion modulo 998244353. Input The primary line contains a solitary integer n (1≤n≤150000). The subsequent line contains 2n integers a1,a2,… ,a2n (1≤ai≤109) — components of exhibit a. Output Print one integer — the response to the issue, modulo 998244353.
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Andre has quite certain preferences. As of late he began becoming hopelessly enamored with clusters. Andre calls a nonempty cluster b great, if amount of its components is distinguishable by the length of this exhibit. For instance, cluster [2,3,1] is acceptable, as amount of its components — 6 — is distinguishable by 3, yet exhibit [1,1,2,3] isn't acceptable, as 7 isn't separable by 4. Andre considers a cluster an of length n great if the accompanying conditions hold: Each nonempty subarray of this cluster is acceptable. For each I (1≤i≤n), 1≤ai≤100. Given a positive integer n, output any ideal cluster of length n. We can show that for the given limitations such a cluster consistently exists. A cluster c is a subarray of an exhibit d if c can be gotten from d by cancellation of a few (conceivably, zero or all) components from the start and a few (perhaps, zero or…
Correct answer will be upvoted else downvoted. Computer science. It might have been a simple undertaking, yet it worked out that you ought to observe a few guidelines: Before all else, you select any sure integer x. Then, at that point, you do the accompanying activity n times: select two components of cluster with total equivalents x; eliminate them from an and supplant x with limit of that two numbers. For instance, if at first a=[3,5,1,2], you can choose x=6. Then, at that point, you can choose the second and the third components of a with total 5+1=6 and toss them out. After this activity, x equivalents 5 and there are two components in cluster: 3 and 2. You can toss them out on the following activity. Note, that you pick x before the beginning and can't transform it as you need between the activities. Decide how could you act to toss out all components of a. Input The main line contains a solitary integer t (1≤t≤1000) — the number of experiments.…
Please answer in c++. Correct answer will upvoted else downvoted. The OmkArray of a cluster a with components a1,a2,… ,a2k−1, is the exhibit b with components b1,b2,… ,bk to such an extent that bi is equivalent to the middle of a1,a2,… ,a2i−1 for all I. Omkar has discovered a cluster b of size n (1≤n≤2⋅105, −109≤bi≤109). Given this cluster b, Ray needs to test Omkar's case and check whether b really is an OmkArray of some exhibit a. Would you be able to help Ray? The middle of a bunch of numbers a1,a2,… ,a2i−1 is the number ci where c1,c2,… ,c2i−1 addresses a1,a2,… ,a2i−1 arranged in nondecreasing request. Input Each test contains various experiments. The main line contains a solitary integer t (1≤t≤104) — the number of experiments. Depiction of the experiments follows. The primary line of each experiment contains an integer n (1≤n≤2⋅105) — the length of the cluster b. The subsequent line contains n integers b1,b2,… ,bn (−109≤bi≤109) — the components of b. It is…
Correct answer will be upvoted else downvoted. Computer science. You are given a cluster an of length n. You are approached to deal with q inquiries of the accompanying organization: given integers I and x, duplicate computer based intelligence by x. In the wake of handling each inquiry you really wanted to output the best normal divisor (GCD) of all components of the cluster a. Since the appropriate response can be excessively huge, you are approached to output it modulo 109+7. Input The principal line contains two integers — n and q (1≤n,q≤2⋅105). The subsequent line contains n integers a1,a2,… ,an (1≤ai≤2⋅105) — the components of the cluster a preceding the changes. The following q lines contain inquiries in the accompanying arrangement: each line contains two integers I and x (1≤i≤n, 1≤x≤2⋅105). Output Print q lines: in the wake of handling each inquiry output the GCD of all components modulo 109+7 on a different line.
you need to write the solutions in python and provide a brief explanation of your codes and the efficiency analysis with comments. 3. Consider a loop tree which is an undirected wighted graph formed by taking a binary tree and adding an edge from exactly one of the leaves to another node in the tree as follows: Letnbe the number of vertices in a loop tree. How long does it take Prim's or Kruskal's algorithms to find the minimum spanning tree in terms ofn? Devise a more efficient algorithm that takes an nxn adjacency weighted matrix as input, and finds the minimum spanning tree of a loop tree. 三 input1 - Not Defteri Dosya Düzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Düzenle Görünü p 14873265 三 input2 - Not Defteri Dosya Düzenle Görünüm0210000200344010000000300000040005604005000000
Which of the following statements are true ? Give reasons for your answers in the form of a short proof or a counter-example. (i) All comparison based sorting algorithms have the same worst case running time. (ii) A topological sort of a Directed Acyclic Graph (DAG) can be created by performing a depth-first-search on the DAG. (iii) o (p) = p\d primes p, where o is the Euler-phi function. (iv) There is a unique min binary heap on the set {1, 2, 9}. ..... (v) Two sequences can have several common subsequences of the length. same maximum