From e0f7da1d15446c21bef26e6433df50b0c599bff9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Radek=20Pu=C5=A1?= <pusradek@fit.cvut.cz>
Date: Sun, 17 Nov 2019 01:39:02 +0100
Subject: [PATCH] Latex - comparator and his testing

---
 Latex/BP_Radek_Pus_2019.pdf  | Bin 644988 -> 700237 bytes
 Latex/BP_Radek_Pus_2019.tex  |  24 ++++++++++++++++++++++++
 Latex/img/ComparatorTest.png | Bin 0 -> 50641 bytes
 3 files changed, 24 insertions(+)
 create mode 100644 Latex/img/ComparatorTest.png

diff --git a/Latex/BP_Radek_Pus_2019.pdf b/Latex/BP_Radek_Pus_2019.pdf
index 37e658b41605e551fbd7c396ccbe4336bab976d1..424c63f661a817d9bf478ce2ececbe353c931a00 100644
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diff --git a/Latex/BP_Radek_Pus_2019.tex b/Latex/BP_Radek_Pus_2019.tex
index ddbb854..c73b935 100644
--- a/Latex/BP_Radek_Pus_2019.tex
+++ b/Latex/BP_Radek_Pus_2019.tex
@@ -304,15 +304,39 @@ První myšlenka, která mnoho lidí napadne, je porovnávání výše transakce
 
 Druhá, související myšlenka, pak bývá: Pokud se nelze orientovat podle ceny, tak je možné se orientovat dle místa, potažmo čísla účtu. Tento případ opět není možný. Budeme-li dále používat Karla jako příklad, řekněme, že si kupuje ráno kávu. Pokud je venku pěkně, jde si ji koupit do stánku kde se prodává levná a dobrá. Musí se ale posadit na lavičku v parku. Pokud ale hezky není jde si ji koupit do kavárny, tedy úplně jiného podniku s úplně jiným číslem účtu. Stejně tak mohl zaspat a kávu si koupí až dotovanou v práci, třebaže mu příliš nechutná. V tom případě si koupil kávu za úplně jinou cenu a ještě na úplně jiném místě s úplně jiným číslem účtu. Všechno to však lze považovat za opakující se transakci.
 
+\subsubsection{Přiřazování do páru}
 Jako možné řešení, které bylo implementováno, tedy je srovnávat transakce ze dvou různých časových úseků. V práci bylo přikloněno k rozsahu jednoho týdne.
 
 Jeden den je příliš malý rozsah, kdy se může stát, že dokonce nedošlo k žádné transakci. Pokud by se porovnával měsíc, transakcí je poměrně mnoho. Běžný člověk má navíc obvykle při opakující se činnosti zažité určité rituály. Nejrozšířenější opakující se činnost bývá chození do práce či školy přes týden. Opakující se rituál potom může být pití kávy po příchodu do práce. Takové činnosti se opakují právě v rámci týdnů a porovnávání by tedy mělo být také v rámci násobků týdnů.
 
 V praxi se rozlišují i aktivity na sudé a liché týdny (cvičení ve škole, pravidelné schůzky v práci, jež se konají ob jeden týden). Ideální by tedy bylo porovnávání transakcí po dvou týdnech. Z nedostatku rozsahu obdržený dat došlo ale k přiklonění se pouze k týdnu jednomu.
 
+Pokud tedy budou uvažovány transakce ze dvou různých týdnů, měla by se opakující se transakce vyskytovat v každém týdnu právě jednou. V jednom z týdnů ale bývá z pravidla transakcí více. Proto by se dalo optimistickým přístupem (člověk po většinu času opakuje činnost) říci, že opakujících se transakcí je právě minimum z počtu transakcí v těchto dvou týdnech. Zároveň jsou v relaci 1:1 - každá opakující se transakce v prvním týdnu má pravě jednu opakující se transakci v týdnu druhém. Zbylé transakce se neopakují.
+
+Pro přiřazování do párů se procházejí v cyklu transakce a ke každé transakci se vybere nějaká, která je ji hodnotou nejblíže. V každém průchodu cyklu se pro každou transakci z menší množiny hledá transakce z množiny větší taková, že rozdíl v jejich částce je nejmenší (tzv. vzdálenost musí být nejkratší). Při hledání těchto dvojic může dojít k duplicitnímu propojení (dvě a více transakcí z jedné množiny, považují jednu transakci z druhé množiny za nejbližší). V tom případě se vezme dvě nejkratší vzdálenosti z tohoto vztahu. Celý cyklus se opakuje, dokud nejsou přiřazeny všechny transakce z menší množiny k množině větší.
+
+\subsubsection{Porovnávání vzdálenosti}
+S touto implementací však vyvstává jeden problém. Toto "optimistické" přiřazování transakcí ve skutečnosti říká, že týden s menší aktivitou je podmnožinou týdne s aktivitou větší. Jinými slovy - všechny platby jednoho z týdnů jsou bezezbytku obsaženy v druhém. To zcela jistě není správně. Opakující se transakce jsou spíše průnikem těchto dvou týdnů (ne všechny se opakují). Je tedy opět třeba se zamyslet, jakým způsobem toto vyřešit.
+
+První možností by bylo omezit počet opakování v cyklu, kdy se párují transakce. Ať už říci, že se cyklus nesmí procházet např. více než třikrát anebo musí zůstat alespoň 5 nerozhodnutých transakcí. Při využití těchto přístupů ale nemám žádnou kontrolu nad samotnými transakcemi. Mohou mi zbýt transakce, které si jsou částkou blízké - to nastává třeba v případě, že dotyčný člověk jednoduše nenakupoval nic navíc a částky jsou si opravdu podmnožinou. Tak je možné, že mezi jednotlivými týdny nebyl finančně příliš aktivní a částek je jen málo - všechny by se mohly vyfiltrovat jako neopakující se. To tedy nepoukazuje na dobré řešení.
+
+Za mnohem korektnější přístup, by se dalo považovat porovnávání ještě podle relativní vzdálenosti jednotlivých částek. Tím je míněno, že hodnoty 10~Kč a 110~Kč se od sebe liší více, než například 5~000~Kč a 5~100~Kč. Obě hodnoty se v absolutním měřítku sice liší jen o sto korun ale částky samotné se pohybují ve zcela jiných řádech. Avšak porovnávání řádů s hodnotou je poměrně abstraktní a jednoduché porovnání řádů s rozdílem částek nejde příliš jednoduše implementovat.
+
+Za řešení lze považovat pohled z hlediska poměrů. Pokud se zůstane u předchozích částek daly by se uvést do poměrů 110~:~10 a 5~100~:~5~000. Poměr pro první zmíněnou částku je roven 11, kdežto pro druhou 1.02. Zde už lze zřetelně vidět, jak moc se od sebe částky relativně liší.
+
+Za povšimnutí však ještě stojí, že je třeba poměřovat vždy částku větší vůči menší, případně naopak. Je však nutné dodržovat pořadí velikostí. Po samotném přiřazení párů navíc není garantováno, která z částek je větší. Mohlo by tedy dojít k tomu, že by se porovnávala čísla normalizovaná do velikosti menší než jedna, s čísly většími než jedna. Takové porovnávání by dávalo zcela nesmyslné výsledky.
+%TODO možná noise
 
 \subsection{Testování komparátoru}
+Ačkoli komparátor, jako takový, je poměrně složitý, jeho výstup už tak složitý není. Vše lze porovnat pouhým okem z výpisu. Příklad vygenerovaného výpisu, s daty z poskytnuté transakční historie, je na obr. č. \ref{ComparatorTest}.
+\begin{figure}[h]
+ 	\includegraphics[width=0.75\textwidth]{img/ComparatorTest.png}
+ 	\centering
+ 	\caption[Test komparátoru]{Test komparátoru}
+ 	\label{ComparatorTest}
+\end{figure}
 
+Lze zde pozorovat, jak se jednotlivé částky na sebe namapovaly (označeno šipkou) a jak jsou od sebe vzdáleny (v závorce). Transakce, které se nepodařilo přiřadit, jsou vypsány v části "Major". Ty jsou tedy označeny za neopakující se.
 \subsection{Datafeeder}
 
 \subsection{Normalizace}
diff --git a/Latex/img/ComparatorTest.png b/Latex/img/ComparatorTest.png
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-- 
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