Диссертация (1148552), страница 20
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133]:1172 ∑=1 min( ) = (3.19. )∑=1 + ∑=1 где ∑=1 min( ) представляет собой сумму минимальных значений из двухклассов, а ∑=1 + ∑=1 - суммы всех значений рассматриваемых совокупностей.Коэффициент Чекановского-Сёренсена принимает значения от 0 до 1, причём онравен 1, когда два объекта полностью совпадают, и 0 – когда два объекта полностьюне совпадают.Аналогично случаю атрибуции при помощи детерминированного алгоритма,для успешного причисления атрибутируемого объекта к априорному классуатрибутируемый объект должен относиться к априорному классу по всемупараметрическомупространству.Классификацияобъектовпроизводитсяводномерном пространстве по каждому параметру отдельно.В качестве исходных данных для атрибуции данным способом используютсяпараметрические описания объекта атрибуции и классов эталонов на языкеинформативных параметров.ДляприменениякритерияЧекановскогоматрицаисходныхданныхформируется следующим образом: каждый вариант сочетания параметров X18, X29,X35 и X52 из рассмотренных в предыдущих разделах выборок будет представлен какодно из значений исследуемого класса, а количество таких сочетаний в выборке – какколичество наблюдений, соответствующих этому значению.Размеры используемых выборок отличаются по величине из-за различногоразмера сравниваемых классов, что теоретически может иметь количественноевлияние на рассчитываемые значения коэффициентов.
Для чистоты эксперимента,данное различие устраняется путём введения дополнительного поправочногокоэффициента 1/n, где n – величина соответствующей выборки. После определенияколичества раз, которое значение X18_X29_X35_X52i встречается в выборке,полученное число умножается на этот коэффициент. Таким образом, формулаопределения коэффициента Сёренсена-Чекановского приобретает вид (3.20)118 ) =(3.20)∑=1 + ∑=12 ∑=1 min(Вычисление коэффициента Сёренсена-Чекановского производится попарно дляклассов «Продолжение Манессье» - «Четвёртое продолжение» и класса «Роман оФиалке» - «Четвёртое продолжение».
Кроме того, также производится расчёткоэффициента для пары «Роман о Фиалке» - «Продолжение Манессье» с цельюпроверкиприменимостикритерияблизостина двухклассахсзаведоморазличающимися авторами.Рассчитанные значения попарных минимумов приведены в таблице 3.27 всокращённом виде, после исключения нулевых значений.Таблица 3.27Определение минимальных значения наблюдений для классов «Четвёртоепродолжение» - «Роман о Фиалке», «Четвёртое продолжение» - «ПродолжениеМанессье», «Продолжение Манессье» - «Роман о Фиалке»Комбинация параметров«Четвёртоепродолжение» «Роман о Фиалке»«Четвёртое продолжение» «Продолжение Манессье»X18 = 0, X29 = 0, X35 = 0, X52 = 00,0480,030«ПродолжениеМанессье» «Роман оФиалке»0,030X18 = 0, X29 = 0, X35 = 0, X52 = 30,0010,0000,000X18 = 0, X29 = 1, X35 = 0, X52 = 00,0500,0440,044X18 = 0, X29 = 1, X35 = 0, X52 = 30,0020,0020,002X18 = 0, X29 = 1, X35 = 0, X52 = 70,0010,0000,000X18 = 0, X29 = 1, X35 = 0, X52 = 80,0020,0000,000X18 = 0, X29 = 10, X35 = 0, X52 = 00,0010,0010,001X18 = 0, X29 = 10, X35 = 0, X52 = 80,0000,0010,000X18 = 0, X29 = 12, X35 = 0, X52 = 00,0000,0010,000X18 = 0, X29 = 13, X35 = 2, X52 = 00,0000,0010,000X18 = 0, X29 = 2, X35 = 0, X52 = 00,0550,0550,055X18 = 0, X29 = 2, X35 = 0, X52 = 50,0000,0010,000X18 = 0, X29 = 2, X35 = 0, X52 = 60,0000,0010,000X18 = 0, X29 = 2, X35 = 0, X52 = 80,0000,0010,000X18 = 0, X29 = 2, X35 = 1, X52 = 00,0030,0050,003X18 = 0, X29 = 3, X35 = 0, X52 = 00,0330,0330,033119X18 = 0, X29 = 3, X35 = 0, X52 = 20,0000,0010,000X18 = 0, X29 = 3, X35 = 0, X52 = 30,0020,0010,001X18 = 0, X29 = 3, X35 = 0, X52 = 60,0000,0010,000X18 = 0, X29 = 3, X35 = 0, X52 = 70,0000,0020,000X18 = 0, X29 = 3, X35 = 0, X52 = 80,0000,0010,000X18 = 0, X29 = 3, X35 = 0, X52 = 90,0010,0000,000X18 = 0, X29 = 3, X35 = 1, X52 = 00,0010,0000,000X18 = 0, X29 = 4, X35 = 0, X52 = 00,0280,0280,028X18 = 0, X29 = 4, X35 = 0, X52 = 30,0010,0010,001X18 = 0, X29 = 4, X35 = 0, X52 = 50,0030,0000,000X18 = 0, X29 = 4, X35 = 0, X52 = 70,0020,0030,002X18 = 0, X29 = 4, X35 = 1, X52 = 00,0030,0020,002X18 = 0, X29 = 5, X35 = 0, X52 = 00,0150,0150,015X18 = 0, X29 = 5, X35 = 0, X52 = 40,0020,0000,000X18 = 0, X29 = 5, X35 = 0, X52 = 50,0000,0010,000X18 = 0, X29 = 5, X35 = 0, X52 = 60,0010,0010,001X18 = 0, X29 = 5, X35 = 0, X52 = 70,0010,0010,001X18 = 0, X29 = 5, X35 = 0, X52 = 90,0020,0010,001X18 = 0, X29 = 5, X35 = 1, X52 = 00,0000,0040,000X18 = 0, X29 = 6, X35 = 0, X52 = 00,0060,0060,006X18 = 0, X29 = 6, X35 = 0, X52 = 50,0010,0010,001X18 = 0, X29 = 6, X35 = 0, X52 = 60,0000,0020,000X18 = 0, X29 = 6, X35 = 1, X52 = 00,0020,0010,001X18 = 0, X29 = 7, X35 = 0, X52 = 00,0030,0050,003X18 = 0, X29 = 7, X35 = 0, X52 = 30,0000,0010,000X18 = 0, X29 = 7, X35 = 0, X52 = 50,0010,0010,001X18 = 0, X29 = 7, X35 = 0, X52 = 80,0010,0010,001X18 = 0, X29 = 7, X35 = 1, X52 = 00,0020,0020,002X18 = 0, X29 = 8, X35 = 0, X52 = 00,0020,0020,002X18 = 0, X29 = 8, X35 = 0, X52 = 30,0010,0000,000X18 = 0, X29 = 9, X35 = 0, X52 = 00,0020,0020,002X18 = 0, X29 = 9, X35 = 0, X52 = 100,0000,0010,000X18 = 1, X29 = 0, X35 = 0, X52 = 00,0030,0040,003X18 = 1, X29 = 0, X35 = 0, X52 = 20,0030,0010,001X18 = 1, X29 = 0, X35 = 0, X52 = 30,0010,0010,001X18 = 1, X29 = 1, X35 = 0, X52 = 00,0030,0030,003X18 = 1, X29 = 1, X35 = 0, X52 = 20,0010,0010,001X18 = 1, X29 = 10, X35 = 0, X52 = 20,0000,0030,000X18 = 1, X29 = 10, X35 = 0, X52 = 70,0000,0010,000X18 = 1, X29 = 11, X35 = 1, X52 = 30,0000,0010,000X18 = 1, X29 = 12, X35 = 0, X52 = 20,0000,0010,000X18 = 1, X29 = 12, X35 = 0, X52 = 60,0000,0010,000X18 = 1, X29 = 13, X35 = 0, X52 = 30,0000,0020,000120X18 = 1, X29 = 2, X35 = 0, X52 = 00,0070,0070,007X18 = 1, X29 = 2, X35 = 0, X52 = 120,0000,0010,000X18 = 1, X29 = 2, X35 = 0, X52 = 20,0090,0090,009X18 = 1, X29 = 2, X35 = 0, X52 = 30,0020,0010,001X18 = 1, X29 = 2, X35 = 0, X52 = 50,0010,0010,001X18 = 1, X29 = 2, X35 = 0, X52 = 60,0000,0010,000X18 = 1, X29 = 3, X35 = 0, X52 = 00,0080,0080,008X18 = 1, X29 = 3, X35 = 0, X52 = 20,0150,0150,015X18 = 1, X29 = 3, X35 = 0, X52 = 30,0060,0050,005X18 = 1, X29 = 3, X35 = 0, X52 = 40,0000,0010,000X18 = 1, X29 = 3, X35 = 0, X52 = 60,0020,0010,001X18 = 1, X29 = 3, X35 = 0, X52 = 70,0000,0010,000X18 = 1, X29 = 3, X35 = 0, X52 = 80,0000,0010,000X18 = 1, X29 = 3, X35 = 0, X52 = 90,0020,0010,001X18 = 1, X29 = 3, X35 = 1, X52 = 00,0020,0010,001X18 = 1, X29 = 3, X35 = 1, X52 = 20,0000,0010,000X18 = 1, X29 = 3, X35 = 1, X52 = 50,0000,0010,000X18 = 1, X29 = 4, X35 = 0, X52 = 00,0050,0050,005X18 = 1, X29 = 4, X35 = 0, X52 = 20,0140,0140,014X18 = 1, X29 = 4, X35 = 0, X52 = 30,0080,0070,007X18 = 1, X29 = 4, X35 = 0, X52 = 40,0000,0020,000X18 = 1, X29 = 4, X35 = 0, X52 = 50,0000,0010,000X18 = 1, X29 = 4, X35 = 0, X52 = 60,0010,0010,001X18 = 1, X29 = 4, X35 = 0, X52 = 70,0020,0010,001X18 = 1, X29 = 4, X35 = 0, X52 = 80,0020,0020,002X18 = 1, X29 = 4, X35 = 0, X52 = 90,0000,0020,000X18 = 1, X29 = 4, X35 = 1, X52 = 00,0010,0000,000X18 = 1, X29 = 4, X35 = 1, X52 = 20,0020,0000,000X18 = 1, X29 = 5, X35 = 0, X52 = 00,0000,0030,000X18 = 1, X29 = 5, X35 = 0, X52 = 100,0000,0020,000X18 = 1, X29 = 5, X35 = 0, X52 = 130,0000,0010,000X18 = 1, X29 = 5, X35 = 0, X52 = 20,0050,0100,005X18 = 1, X29 = 5, X35 = 0, X52 = 30,0070,0050,005X18 = 1, X29 = 5, X35 = 0, X52 = 40,0020,0020,002X18 = 1, X29 = 5, X35 = 0, X52 = 50,0020,0020,002X18 = 1, X29 = 5, X35 = 0, X52 = 60,0000,0020,000X18 = 1, X29 = 5, X35 = 0, X52 = 80,0000,0010,000X18 = 1, X29 = 5, X35 = 0, X52 = 90,0000,0020,000X18 = 1, X29 = 5, X35 = 1, X52 = 00,0000,0010,000X18 = 1, X29 = 5, X35 = 1, X52 = 20,0020,0010,001X18 = 1, X29 = 5, X35 = 1, X52 = 30,0000,0010,000X18 = 1, X29 = 6, X35 = 0, X52 = 00,0030,0020,002X18 = 1, X29 = 6, X35 = 0, X52 = 100,0000,0010,000121X18 = 1, X29 = 6, X35 = 0, X52 = 20,0020,0100,002X18 = 1, X29 = 6, X35 = 0, X52 = 30,0030,0040,003X18 = 1, X29 = 6, X35 = 0, X52 = 40,0020,0000,000X18 = 1, X29 = 6, X35 = 0, X52 = 50,0020,0010,001X18 = 1, X29 = 6, X35 = 0, X52 = 60,0000,0010,000X18 = 1, X29 = 6, X35 = 0, X52 = 70,0020,0020,002X18 = 1, X29 = 6, X35 = 0, X52 = 80,0020,0010,001X18 = 1, X29 = 6, X35 = 0, X52 = 90,0010,0010,001X18 = 1, X29 = 6, X35 = 1, X52 = 20,0000,0010,000X18 = 1, X29 = 6, X35 = 1, X52 = 30,0000,0010,000X18 = 1, X29 = 7, X35 = 0, X52 = 00,0020,0020,002X18 = 1, X29 = 7, X35 = 0, X52 = 140,0010,0000,000X18 = 1, X29 = 7, X35 = 0, X52 = 20,0020,0040,002X18 = 1, X29 = 7, X35 = 0, X52 = 30,0030,0040,003X18 = 1, X29 = 7, X35 = 0, X52 = 40,0020,0000,000X18 = 1, X29 = 7, X35 = 0, X52 = 50,0000,0010,000X18 = 1, X29 = 7, X35 = 0, X52 = 80,0020,0000,000X18 = 1, X29 = 7, X35 = 0, X52 = 90,0000,0010,000X18 = 1, X29 = 7, X35 = 1, X52 = 30,0010,0000,000X18 = 1, X29 = 8, X35 = 0, X52 = 00,0000,0010,000X18 = 1, X29 = 8, X35 = 0, X52 = 20,0020,0030,002X18 = 1, X29 = 8, X35 = 0, X52 = 30,0050,0000,000X18 = 1, X29 = 8, X35 = 0, X52 = 40,0000,0010,000X18 = 1, X29 = 8, X35 = 0, X52 = 60,0000,0010,000X18 = 1, X29 = 8, X35 = 0, X52 = 90,0000,0010,000X18 = 1, X29 = 9, X35 = 0, X52 = 00,0000,0010,000X18 = 1, X29 = 9, X35 = 0, X52 = 30,0000,0020,000X18 = 1, X29 = 9, X35 = 1, X52 = 20,0020,0000,000X18 = 2, X29 = 0, X35 = 0, X52 = 00,0020,0020,002X18 = 2, X29 = 0, X35 = 0, X52 = 20,0010,0000,000X18 = 2, X29 = 0, X35 = 1, X52 = 00,0010,0000,000X18 = 2, X29 = 1, X35 = 0, X52 = 00,0020,0030,002X18 = 2, X29 = 1, X35 = 0, X52 = 90,0000,0010,000X18 = 2, X29 = 1, X35 = 1, X52 = 0X18 = 2, X29 = 10, X35 = 0, X52 =150,0000,0010,0000,0000,0010,000X18 = 2, X29 = 10, X35 = 0, X52 = 50,0000,0010,000X18 = 2, X29 = 10, X35 = 0, X52 = 8X18 = 2, X29 = 11, X35 = 0, X52 =12X18 = 2, X29 = 11, X35 = 0, X52 =220,0000,0010,0000,0000,0010,0000,0010,0000,000X18 = 2, X29 = 11, X35 = 0, X52 = 30,0010,0000,000X18 = 2, X29 = 11, X35 = 0, X52 = 50,0000,0010,000122X18 = 2, X29 = 11, X35 = 0, X52 = 6X18 = 2, X29 = 11, X35 = 1, X52 =12X18 = 2, X29 = 12, X35 = 0, X52 =110,0000,0010,0000,0010,0000,0000,0010,0000,000X18 = 2, X29 = 15, X35 = 0, X52 = 40,0010,0000,000X18 = 2, X29 = 2, X35 = 0, X52 = 00,0050,0050,005X18 = 2, X29 = 2, X35 = 0, X52 = 20,0010,0000,000X18 = 2, X29 = 2, X35 = 0, X52 = 30,0020,0020,002X18 = 2, X29 = 2, X35 = 0, X52 = 50,0000,0010,000X18 = 2, X29 = 3, X35 = 0, X52 = 00,0000,0030,000X18 = 2, X29 = 3, X35 = 0, X52 = 20,0000,0010,000X18 = 2, X29 = 3, X35 = 0, X52 = 30,0010,0010,001X18 = 2, X29 = 3, X35 = 0, X52 = 40,0000,0010,000X18 = 2, X29 = 3, X35 = 0, X52 = 50,0020,0000,000X18 = 2, X29 = 3, X35 = 0, X52 = 70,0000,0010,000X18 = 2, X29 = 3, X35 = 0, X52 = 90,0020,0000,000X18 = 2, X29 = 4, X35 = 0, X52 = 00,0030,0020,002X18 = 2, X29 = 4, X35 = 0, X52 = 30,0040,0020,002X18 = 2, X29 = 4, X35 = 0, X52 = 40,0000,0030,000X18 = 2, X29 = 4, X35 = 0, X52 = 50,0030,0020,002X18 = 2, X29 = 4, X35 = 1, X52 = 40,0000,0010,000X18 = 2, X29 = 5, X35 = 0, X52 = 30,0010,0010,001X18 = 2, X29 = 5, X35 = 0, X52 = 40,0000,0050,000X18 = 2, X29 = 5, X35 = 0, X52 = 50,0070,0030,003X18 = 2, X29 = 5, X35 = 0, X52 = 60,0020,0010,001X18 = 2, X29 = 5, X35 = 0, X52 = 90,0020,0000,000X18 = 2, X29 = 5, X35 = 1, X52 = 00,0010,0000,000X18 = 2, X29 = 5, X35 = 1, X52 = 30,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 00,0010,0010,001X18 = 2, X29 = 6, X35 = 0, X52 = 100,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 110,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 120,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 130,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 20,0030,0020,002X18 = 2, X29 = 6, X35 = 0, X52 = 30,0000,0010,000X18 = 2, X29 = 6, X35 = 0, X52 = 40,0000,0020,000X18 = 2, X29 = 6, X35 = 0, X52 = 50,0030,0030,003X18 = 2, X29 = 6, X35 = 0, X52 = 60,0020,0000,000X18 = 2, X29 = 6, X35 = 0, X52 = 80,0000,0010,000X18 = 2, X29 = 6, X35 = 1, X52 = 20,0010,0000,000X18 = 2, X29 = 6, X35 = 1, X52 = 40,0010,0010,001X18 = 2, X29 = 7, X35 = 0, X52 = 20,0030,0000,000X18 = 2, X29 = 7, X35 = 0, X52 = 30,0000,0020,000123X18 = 2, X29 = 7, X35 = 0, X52 = 40,0020,0010,001X18 = 2, X29 = 7, X35 = 0, X52 = 50,0000,0010,000X18 = 2, X29 = 7, X35 = 0, X52 = 80,0000,0010,000X18 = 2, X29 = 7, X35 = 0, X52 = 90,0020,0000,000X18 = 2, X29 = 7, X35 = 1, X52 = 40,0000,0020,000X18 = 2, X29 = 8, X35 = 0, X52 = 100,0000,0010,000X18 = 2, X29 = 8, X35 = 0, X52 = 50,0010,0010,001X18 = 2, X29 = 8, X35 = 0, X52 = 60,0010,0010,001X18 = 2, X29 = 8, X35 = 0, X52 = 70,0000,0010,000X18 = 2, X29 = 8, X35 = 0, X52 = 80,0020,0010,001X18 = 2, X29 = 8, X35 = 0, X52 = 90,0000,0010,000X18 = 2, X29 = 8, X35 = 1, X52 = 40,0010,0000,000X18 = 2, X29 = 9, X35 = 0, X52 = 60,0020,0020,002X18 = 2, X29 = 9, X35 = 0, X52 = 70,0000,0010,000X18 = 2, X29 = 9, X35 = 1, X52 = 40,0000,0010,000X18 = 2, X29 = 9, X35 = 1, X52 = 60,0000,0010,000X18 = 3, X29 = 0, X35 = 0, X52 = 20,0000,0010,000X18 = 3, X29 = 11, X35 = 0, X52 = 70,0010,0010,001X18 = 3, X29 = 11, X35 = 0, X52 = 80,0000,0010,000X18 = 3, X29 = 12, X35 = 0, X52 = 20,0000,0010,000X18 = 3, X29 = 2, X35 = 0, X52 = 20,0020,0000,000X18 = 3, X29 = 2, X35 = 0, X52 = 30,0010,0000,000X18 = 3, X29 = 3, X35 = 0, X52 = 00,0000,0010,000X18 = 3, X29 = 3, X35 = 0, X52 = 80,0010,0000,000X18 = 3, X29 = 3, X35 = 1, X52 = 60,0010,0000,000X18 = 3, X29 = 4, X35 = 0, X52 = 40,0020,0020,002X18 = 3, X29 = 5, X35 = 0, X52 = 100,0010,0000,000X18 = 3, X29 = 5, X35 = 0, X52 = 20,0000,0010,000X18 = 3, X29 = 5, X35 = 0, X52 = 50,0010,0010,001X18 = 3, X29 = 6, X35 = 0, X52 = 70,0000,0010,000X18 = 3, X29 = 7, X35 = 0, X52 = 110,0000,0010,000X18 = 3, X29 = 7, X35 = 0, X52 = 50,0000,0010,000X18 = 3, X29 = 7, X35 = 0, X52 = 70,0010,0000,000X18 = 3, X29 = 7, X35 = 0, X52 = 80,0020,0010,001X18 = 3, X29 = 7, X35 = 0, X52 = 90,0000,0010,000X18 = 3, X29 = 8, X35 = 0, X52 = 100,0000,0010,000X18 = 3, X29 = 8, X35 = 0, X52 = 3X18 = 4, X29 = 10, X35 = 0, X52 =120,0000,0010,0000,0000,0010,000X18 = 4, X29 = 10, X35 = 0, X52 = 90,0000,0010,000X18 = 4, X29 = 3, X35 = 0, X52 = 50,0000,0010,000X18 = 4, X29 = 7, X35 = 0, X52 = 80,0000,0010,000X18 = 4, X29 = 7, X35 = 1, X52 = 80,0010,0000,000124X18 = 4, X29 = 8, X35 = 0, X52 = 150,0000,0010,000X18 = 4, X29 = 9, X35 = 1, X52 = 60,0000,0010,000X18 = 5, X29 = 6, X35 = 0, X52 = 100,0010,0000,000Так как суммарное значение по каждому классу равно 1, то нулевые значенияне вносят вклад в величину коэффициента, и значение коэффициента равно суммеминимальных количеств наблюдений каждого значения.