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Mahalanobis mesafesi<\/strong> \u00e7ok de\u011fi\u015fkenli bir uzayda iki nokta aras\u0131ndaki mesafedir. Birden fazla de\u011fi\u015fkeni i\u00e7eren istatistiksel analizlerde ayk\u0131r\u0131 de\u011ferleri tespit etmek i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r.<\/span><\/p>\n Bu e\u011fitimde Python’da Mahalanobis mesafesinin nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n Python’da bir veri k\u00fcmesindeki her g\u00f6zlemin Mahalanobis mesafesini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullan\u0131n.<\/span><\/p>\n Ad\u0131m 1: Veri k\u00fcmesini olu\u015fturun.<\/strong><\/span><\/p>\n \u0130lk olarak 20 \u00f6\u011frencinin s\u0131nav puanlar\u0131n\u0131, ders \u00e7al\u0131\u015farak ge\u00e7irdikleri saat say\u0131s\u0131n\u0131, girdikleri uygulama s\u0131nav say\u0131s\u0131n\u0131 ve dersteki mevcut notlar\u0131n\u0131 g\u00f6steren bir veri seti olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n Ad\u0131m 2: Her g\u00f6zlem i\u00e7in Mahalanobis mesafesini hesaplay\u0131n.<\/strong><\/span><\/p>\n Daha sonra Mahalanobis mesafesini hesaplamak i\u00e7in k\u0131sa bir fonksiyon yazaca\u011f\u0131z.<\/span><\/p>\n Ad\u0131m 3: Her Mahalanobis mesafesi i\u00e7in p de\u011ferini hesaplay\u0131n.<\/strong><\/span><\/p>\n Baz\u0131 Mahalanobis mesafelerinin di\u011ferlerinden \u00e7ok daha b\u00fcy\u00fck oldu\u011funu g\u00f6rebiliriz. Mesafelerden herhangi birinin istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in p de\u011ferlerini hesaplamam\u0131z gerekir.<\/span><\/p>\n Her mesafe i\u00e7in p de\u011feri, k = de\u011fi\u015fken say\u0131s\u0131 olmak \u00fczere, k-1 serbestlik derecesine sahip Mahalanobis mesafesinin ki-kare istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri olarak hesaplan\u0131r. Bu durumda serbestlik derecesi 4-1 = 3’\u00fc kullanaca\u011f\u0131z.<\/span><\/p>\n Genellikle 0,001’den k\u00fc\u00e7\u00fck<\/strong> bir p de\u011feri ayk\u0131r\u0131 de\u011fer olarak kabul edilir.<\/span> \u0130lk g\u00f6zlemin veri setinde bir ayk\u0131r\u0131 de\u011fer oldu\u011funu g\u00f6rebiliriz \u00e7\u00fcnk\u00fc p de\u011feri 0,001’den k\u00fc\u00e7\u00fckt\u00fcr.<\/span><\/p>\n Sorunun ba\u011flam\u0131na ba\u011fl\u0131 olarak, ayk\u0131r\u0131 bir de\u011fer oldu\u011fundan ve analiz sonu\u00e7lar\u0131n\u0131 etkileyebilece\u011finden bu g\u00f6zlemi veri k\u00fcmesinden \u00e7\u0131karmaya karar verebilirsiniz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" Mahalanobis mesafesi \u00e7ok de\u011fi\u015fkenli bir uzayda iki nokta aras\u0131ndaki mesafedir. Birden fazla de\u011fi\u015fkeni i\u00e7eren istatistiksel analizlerde ayk\u0131r\u0131 de\u011ferleri tespit etmek i\u00e7in s\u0131kl\u0131kla kullan\u0131l\u0131r. Bu e\u011fitimde Python’da Mahalanobis mesafesinin nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. \u00d6rnek: Python’da Mahalanobis Mesafesi Python’da bir veri k\u00fcmesindeki her g\u00f6zlemin Mahalanobis mesafesini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullan\u0131n. Ad\u0131m 1: Veri k\u00fcmesini olu\u015fturun. \u0130lk olarak […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-832","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n \u00d6rnek: Python’da Mahalanobis Mesafesi<\/strong><\/span><\/h3>\n
import<\/span> numpy as<\/span> np\nimport<\/span> pandas as<\/span> pd\nimport<\/span> scipy as<\/span> stats\n\ndata = {'score': [91, 93, 72, 87, 86, 73, 68, 87, 78, 99, 95, 76, 84, 96, 76, 80, 83, 84, 73, 74],\n 'hours': [16, 6, 3, 1, 2, 3, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 4, 3, 4, 4],\n 'prep': [3, 4, 0, 3, 4, 0, 1, 2, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2],\n 'grade': [70, 88, 80, 83, 88, 84, 78, 94, 90, 93, 89, 82, 95, 94, 81, 93, 93, 90, 89, 89]\n }\n\ndf = pd.DataFrame(data,columns=['score', 'hours', 'prep','grade'])\ndf.head()\n\n score hours prep grade\n0 91 16 3 70\n1 93 6 4 88\n2 72 3 0 80\n3 87 1 3 83\n4 86 2 4 88\n<\/strong><\/pre>\n #create function to calculate Mahalanobis distance<\/span>\ndef<\/span> mahalanobis(x= None<\/span> , data= None<\/span> , cov= None<\/span> ):\n\n x_mu = x - np.mean(data)\n if not cov:\n cov = np.cov(data.values.T)\n inv_covmat = np.linalg.inv(cov)\n left = np.dot(x_mu, inv_covmat)\n mahal = np.dot(left, x_mu.T)\n return mahal.diagonal()\n\n#create new column in dataframe that contains Mahalanobis distance for each row<\/span><\/span>\ndf['mahalanobis'] = mahalanobis(x=df, data=df[['score', 'hours', 'prep', 'grade']])\n\n#display first five rows of dataframe\n<\/span>df.head()\n\n score hours prep grade mahalanobis\n0 91 16 3 70 16.501963\n1 93 6 4 88 2.639286\n2 72 3 0 80 4.850797\n3 87 1 3 83 5.201261\n4 86 2 4 88 3.828734\n<\/strong><\/pre>\n from<\/span> scipy.stats import<\/span> chi2\n\n#calculate p-value for each mahalanobis distance<\/span> \ndf['p'] = 1 - chi2.cdf(df['mahalanobis'], 3)\n\n#display p-values for first five rows in dataframe<\/span>\ndf.head()\n\n score hours prep grade mahalanobis p\n0 91 16 3 70 16.501963 0.000895\n1 93 6 4 88 2.639286 0.450644\n2 72 3 0 80 4.850797 0.183054\n3 87 1 3 83 5.201261 0.157639\n4 86 2 4 88 3.828734 0.280562\n<\/strong><\/pre>\n