Delne urejenosti in hierarhično gručenje

Ferk, Eva

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Title:	Delne urejenosti in hierarhično gručenje
Authors:	ID Ferk, Eva (Author) ID Bokal, Drago (Mentor) More about this mentor... ID Rizman Žalik, Krista (Mentor) More about this mentor...
Files:	UNI_Ferk_Eva_2009.pdf (4,59 MB) MD5: 1770864545B67BDF718C55CC0454B554 PID: 20.500.12556/dkum/d2b94130-b30d-449d-bf48-8dfdf9c245ff
Language:	Slovenian
Work type:	Undergraduate thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	Gručenje podatkov velja za eno najpomembnejših metod podatkovnega rudarjenja, ki se kot nova informacijska tehnologija dnevno razvija. Razvrščanja objektov v gruče so se tekom let raziskovalci lotevali na več načinov, kar s seboj prinese obilico različnih metod in postopkov. V diplomski nalogi se podrobneje seznanimo z merili za podobnost objektov znotraj posamezne gruče. Predstavljenih je več metod, od tega so tri hierarhične metode implementirane, predstavljene pa so tudi razlike med njimi. Vsaka razvrstitev objektov v gruče je matematično gledano ekvivalenčna relacija. Dva podatka sta ekvivalentna, če sta v isti gruči. V prvem delu je razvito matematično orodje, s katerim kasneje raziskujemo lastnosti podatkovne hierarhije, ki nastane med izvajanjem algoritmov gručenja. Končna ugotovitev kaže na to, da je reducirani graf podatkovne hierarhije, ki ga dobimo tekom razvrščanja hierarhičnih algoritmov gručenja, enak poti, za nehiearhično metodo $K$-voditeljev pa je to graf brez povezav.
Keywords:	podatkovna hierarhija, gručenje podatkov, delne urejenosti, dendrogram, ugnezdeni gručni diagram, ekvivalenčna relacija, minimalna metoda, maksimalna metoda, povprečna metoda
Place of publishing:	Maribor
Publisher:	[E. Ferk]
Year of publishing:	2009
PID:	20.500.12556/DKUM-9968
UDC:	51(043.2)
COBISS.SI-ID:	16751368
NUK URN:	URN:SI:UM:DK:PFJCOTVV
Publication date in DKUM:	22.04.2009
Views:	5450
Downloads:	534
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	Partial orders and hierarchical clustering
Abstract:	Data clustering is the task of organizing a set of object into groups (clusters) according to some similarity measure of the objects. As such, data clustering represents one of the most important methods of data mining. Over the years, the researchers have classified objects into clusters in several ways, which brings up plenty of different methods and procedures. In this graduation thesis, we implemented three hierarchical clustering methods and studied differences between them. Each classification of objects is from mathematical point of view an equivalence relation. Two data objects are equivalent if they are in the same cluster. In the first part, a mathematical framework of data hierarchies is developed. It enables us to study characteristics of data hierarchy, which we obtain during the execution of clustering algorithms. We show that reduced graph of data hierarchy, which results from execution of a hierarchical clustering algorithm, is a path. During nonhierarchical algorithm of K-means we obtain a graph without edges.
Keywords:	Data hierarchy, clustering, partial order, dendrogram, nested cluster diagram, equivalence relation, single link, complete link, group-average agglomerative clustering.

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