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The document includes an academic integrity statement and signature area, followed by multiple True/False statements assessing algorithms such as Gaussian Mixture Models, K-means, ISOMAP, t-SNE, PCA, Random Projection, spectral clustering, CCA, and EM. It also contains multiple-choice questions about linear projection distance preservation properties, and about ISOMAP and spectral embedding behavior on regular graphs, with answer selections and brief justifications.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/cs4786-midterm-spring-2019-true-or-false-multiple-choice-questions/395034/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/cs4786-midterm-spring-2019-true-or-false-multiple-choice-questions/395034.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-26",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the document’s main structure and question types?","Question",{"text":112,"@type":113},"It is organized into a section of True/False statements and a second section of Multiple Choice Questions, with instructions for selecting the correct options.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which algorithms are referenced in the True/False section?",{"text":117,"@type":113},"The True/False items mention Gaussian Mixture Models, K-means, single-link clustering, ISOMAP, t-SNE, PCA, Random Projection, normalized spectral clustering, CCA, kernel PCA, and EM.",{"name":119,"@type":110,"acceptedAnswer":120},"What topics do the Multiple Choice Questions focus on?",{"text":121,"@type":113},"They address properties of linear dimensionality reduction (distance preservation under orthonormal projections), correctness goals of ISOMAP, and when normalized versus unnormalized spectral embeddings match for regular graphs.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},395034,1790528217,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":41,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","CS4786 Midterm (Practice)  \nSpring 2019  \n\n| NAME: |  |\n| --- | --- |\n| Net ID: |  |\n| Email: |  |\n\nI promise to abide by Cornell's Code of Academic Integrity.  \nSignature:    \n1 [15] True or False  \nPlease identify if these statements are either True or False.  \n1. Of the clustering algorithms covered in class, Gaussian Mixture Models used for clustering always outperformsk-means and single link clustering.  \nF. Even in practice, the structure in underlying data dictates which algorithm is better for your problem.  \n2. K-means algorithm always 􀀌nds the clustering (C1 ; : : : ; CK ) that minimizes the objective:  \nK  \nMinimize X X kxt 􀀀 rj k2 where rj =  1  X xt is the centroid of cluster jk=1 t2Cj j Cj j t2Cj  \nF. K-means algorithm is only guaranteed to not make the objective worse. So it need not exactly minimize objective. It can get stuck in local minima.  \n3. If in the ISOMAP algorithm, one changes the nearest neighbor graph to a weighted graph with edge weight between two vertices i; j to be  \npi!7j + pj!7i   exp 􀀐 􀀀 ~~ ~~kxix~~2~~jk2 􀀑   \nPi;j = 2n where pi!7j = Pki exp 􀀐 􀀀 ~~ ~~kx~~i~~x~~2k~~k2 􀀑  \nthen one can recover t-SNE algorithm.  \nF.  \n4. PCA can for some dataset approximately preserve pairwise distances between all pairs of points.  \nT. If data is low dimensional.  \n5. Random Projection can always approximately preserve pairwise distances between all pairs of points.  \nT JL theorem proves this.  \n6. Normalized Spectral clustering can only be applied to unweighted and undirected graphs  \nF  \n7. Since PCA computes largest K eigenvectors of the covariance matrix 􀀆, it requires computation time of at least order d2  \nF. Using SVD, in the case when n \u003C\u003C d, we can get computation time to be linear in d  \n8. CCA algorithm is always translation and rotation invariant. T  \n9. In kernel PCA, the larger the dimensionality of feature space (i.e. dimensionality of 􀀈(xt )'s), the longer kernel PCA will take to run. F.  \n10. EM algorithm can only be used for parameter estimation of mixture models. F.  \n11. Dimensionality reduction can be used to remove noise from high dimensional data. T.  \n12. Say data lies on a two dimensional circle embedded in a d-dimensional space, then performing classical PCA and reducing d dimension to 2 dimensions does note lead to loss of information T.  \n13. Random projection guarantees that distances between all pairs of points is preserved even when data in the higher dimension lies on a non-linear manifold. T.  \n14. Laplacian matrix of a graph is always positive semide􀀌nite. T. 15. Sample covariance matrix of a set of n  \npoints in d dimensions is a d 􀀂 d matrix. T.  \n2 [20] Multiple Choice Questions  \nTick the right one(s) . More than one choice can be correct.  \n1. Consider a linear dimensionality reduction method, where we obtain low dimensional (K dimensional) projection yt of point xt in d dimensions by setting y = x>tW for some projection matrix W of dimension d 􀀂 K. Further, say W were such that its columns were orthogonal to each other and have unit norm. That is, if Wkis the k'th column of W , then Wk ? Wj for any j; k and kWkk2 = 1 (Eg. PCA, CCA, . . . ) . Which of the following are true for such linear dimensionality reduction methods:  \nA. Any such method can always guarantee that if K \u003C\u003C d is large enough, then all pairwise distances between points are always approximately preserved?  \nB. It is possible to choose a particular W as above such that if K \u003C d is chosen large enough, then all pairwise distances between points are always approximately preserved?  \nC. It is possible to choose a particular W as above such that if K \u003C d is chosen large enough, for some datasets distances are always approximately preserved?  \nD. PCA algorithm is one example of linear projection as speci􀀌ed in the question that can, for some dataset preserve all pairwise distances between points approximately.  \nA and B are false. If kWkk2 = 1 then in direction of Wk magnitude is exactly preserved and in all o","cbCaitKidVoyF3Gt","https://ap.wps.com/l/cbCaitKidVoyF3Gt","pdf",272771,12,"English","# True or False Questions\n## Multiple Choice Questions","[{\"question\":\"What is the document’s main structure and question types?\",\"answer\":\"It is organized into a section of True/False statements and a second section of Multiple Choice Questions, with instructions for selecting the correct options.\"},{\"question\":\"Which algorithms are referenced in the True/False section?\",\"answer\":\"The True/False items mention Gaussian Mixture Models, K-means, single-link clustering, ISOMAP, t-SNE, PCA, Random Projection, normalized spectral clustering, CCA, kernel PCA, and EM.\"},{\"question\":\"What topics do the Multiple Choice Questions focus on?\",\"answer\":\"They address properties of linear dimensionality reduction (distance preservation under orthonormal projections), correctness goals of ISOMAP, and when normalized versus unnormalized spectral embeddings match for regular graphs.\"}]","CS4786 Midterm - Spring 2019 - True or False & Multiple Choice Questions | PDF",1790415504]