VIDEO solution: Which value of k in the k-nearest neighbors algorithm generates the solid decision boundary depicted here? There are only 2 classes. (Ignore the dashed line, which is the Bayes decision boundary.) k = 1, k = 10, k = 2, k = 100. 0. i. ii. (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "NdOkWtMQ29P0NyGR44gRlopYuJkzmwGDsa5epJo0fH17Z2iUDMbtGmf9DbhKjpo0"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; if (is_login) { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "NdOkWtMQ29P0NyGR44gRlopYuJkzmwGDsa5epJo0fH17Z2iUDMbtGmf9DbhKjpo0"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } else { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { anon_pretype(); } else { $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "NdOkWtMQ29P0NyGR44gRlopYuJkzmwGDsa5epJo0fH17Z2iUDMbtGmf9DbhKjpo0"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; build_popup(); }, error: function(response){ console.log(response); } }); } } } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "NdOkWtMQ29P0NyGR44gRlopYuJkzmwGDsa5epJo0fH17Z2iUDMbtGmf9DbhKjpo0", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    VIDEO solution: Which value of k in the k-nearest neighbors algorithm generates the solid decision boundary depicted here? There are only 2 classes. (Ignore the dashed line, which is the Bayes decision boundary.) k = 1, k = 10, k = 2, k = 100.

0.

i. ii. (2024)

    FAQs

    What is the K value in the KNN algorithm? ›

    The k value in the k-NN algorithm defines how many neighbors will be checked to determine the classification of a specific query point. For example, if k=1, the instance will be assigned to the same class as its single nearest neighbor.

    How to calculate k nearest neighbor? ›

    Step-1: Select the number K of the neighbors. Step-2: Calculate the Euclidean distance of K number of neighbors. Step-3: Take the K nearest neighbors as per the calculated Euclidean distance. Step-4: Among these k neighbors, count the number of the data points in each category.

    What is the decision boundary of K nearest neighbors? ›

    The decision boundary in k-NN is a crucial concept that separates different classes in the feature space. It is the line, surface, or hypersurface that determines the class label assigned to a data point based on the majority class of its k-nearest neighbors.

    What is the K nearest neighbor algorithm? ›

    The K-Nearest Neighbors (KNN) algorithm is a popular machine learning technique used for classification and regression tasks. It relies on the idea that similar data points tend to have similar labels or values.

    What is K 3 in KNN? ›

    3.1: K nearest neighbors

    If we choose K=3, then we have 2 observations in Class B and one observation in Class A. So, we classify the red star to Class B. If we choose K=6, then we have 2 observations in Class B but four observations in Class A.

    What is K 5 in KNN? ›

    kNN classifier identifies the class of a data point using the majority voting principle. If k is set to 5, the classes of 5 nearest points are examined. Prediction is done according to the predominant class. Similarly, kNN regression takes the mean value of 5 nearest locations.

    Does kNN work with categorical variables? ›

    Among the three classification methods, only Kernel Density Classification can handle the categorical variables in theory, while kNN and SVM are unable to be applied directly since they are based on the Euclidean distances.

    How do you solve the nearest neighbor algorithm? ›

    These are the steps of the algorithm:
    1. Initialize all vertices as unvisited.
    2. Select an arbitrary vertex, set it as the current vertex u. ...
    3. Find out the shortest edge connecting the current vertex u and an unvisited vertex v.
    4. Set v as the current vertex u. ...
    5. If all the vertices in the domain are visited, then terminate.

    How does K nearest neighbors algorithm work? ›

    The KNN algorithm uses 'feature similarity' to predict the values of any new data points. This means that the new point is assigned a value based on how closely it resembles the points in the training set.

    What is the decision boundary formula? ›

    Decision Boundary - What is the decision boundary formula? In a basic binary logistic regression model with two features, the formula for the decision boundary is: 0 = β0 + β1*x1 + β2*x2. In this equation, β0, β1, and β2 are the model parameters, and x1 and x2 represent the two features.

    What is k-nearest neighbor for beginners? ›

    K-Nearest Neighbors is one of the simplest supervised machine learning algorithms used for classification. It classifies a data point based on its neighbors' classifications. It stores all available cases and classifies new cases based on similar features.

    What is the fastest K nearest neighbor algorithm? ›

    To the best of our knowledge, EFANNA is the fastest algorithm so far both on approximate nearest neighbor graph construction and approximate nearest neighbor search. A library EFANNA based on this research is released on Github. Index Terms—Approximate nearest neighbor search, approximate kNN graph construction.

    Is k-nearest neighbor a lazy algorithm? ›

    KNN is a typical example of a lazy learner. It is called lazy not because of its apparent simplicity, but because it doesn't learn a discriminative function from the training data but memorizes the training dataset instead.

    What is the difference between K nearest neighbor algorithm? ›

    These two algorithms are often confused due to the letter 'K' in both of them; however, both are different from each other. KNN is a supervised machine learning algorithm, while on the other hand, K-Means is an unsupervised machine learning algorithm.

    Why the value of k is odd in KNN? ›

    Why is the odd value of “K” preferred over even values in the KNN Algorithm? The odd value of K should be preferred over even values in order to ensure that there are no ties in the voting. If the square root of a number of data points is even, then add or subtract 1 to it to make it odd.

    Is k means and KNN the same? ›

    These two algorithms are often confused due to the letter 'K' in both of them; however, both are different from each other. KNN is a supervised machine learning algorithm, while on the other hand, K-Means is an unsupervised machine learning algorithm.

    What is K nearest neighbor optimization? ›

    K-Nearest Neighbors algorithm (KNN) is one of the simplest algorithms; it is widely used in predictive analysis. To optimize its performance and to accelerate its process, this paper proposes a new solution to speed up KNN algorithm based on clustering and attributes filtering.

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