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index.md

@@ -1 +1,7 @@
-# DATAMINING
+# Datamining
+## CONTENTS
+- [ASSOCIATION_RULES](pages/association_rules/ASSOCIATION_RULES.md)
+- [CLASSIFICATION](pages/classification/CLASSIFICATION.md)
+- [CLUSTERING](pages/clustering/CLUSTERING.md)
+- [BUSINESS_INTELLIGENCE_AND_DATA_WAREHOUSE](pages/datamining_process/BUSINESS_INTELLIGENCE_AND_DATA_WAREHOUSE.md)
+- [DATA_PREPROCESSING](pages/preprocessing/DATA_PREPROCESSING.md)

pages/association_rules/APRIORI ALGORITHM.md → pages/association_rules/APRIORI_ALGORITHM.md

@@ -1,10 +1,23 @@
+---
+id: APRIORI_ALGORITHM
+aliases: []
+tags: []
+---
+
+- [~] ---
+id: APRIORI ALGORITHM
+aliases: []
+tags: []
+index: 5
+---
+
 # APRIORI ALGORITHM
 
-The apriori algorithm is a strategy to prune the three of candidates of the [frequent item-set generation](FREQUENT%20ITEMSET%20GENERATION.md) fase it's based on the apriori priciple
+The apriori algorithm is a strategy to prune the three of candidates of the [frequent item-set generation](FREQUENT_ITEMSET_GENERATION.md) fase it's based on the apriori priciple
 
 ### APRIORI PRINCIPLE
 If an itemset is frequent, then all of its subsets must also be frequent and viceversa.
-We can see this principle as follows: 
+We can see this principle as follows:
 
 $$
 \forall X,Y: (X \subset Y) \implies sup(X) \geq sup(Y)
@@ -26,4 +39,6 @@ flowchart TD
 	C-->|repeat until the current level is empty|A
 ```
 
-The $threshold$ value it's an important tuning parameter for complexity and the tradeoff element between number of valid time-sets founded and quality of the item-sets founded 
+The $threshold$ value it's an important tuning parameter for complexity and the tradeoff element between number of valid time-sets founded and quality of the item-sets founded
+
+[PREVIOUS](FREQUENT_ITEMSET_GENERATION.md) [NEXT](FP-GROWTH.md)

pages/association_rules/ASSOCIATION RULES.md → pages/association_rules/ASSOCIATION_RULES.md

@@ -1,3 +1,10 @@
+---
+id: ASSOCIATION RULES
+aliases: []
+tags: []
+index: 1
+---
+
 # ASSOCIATION RULES
 
 They are rules that describes situation where the presence of a given element $\{A\}$ or a combination of elements $\{A,B\}$ assure the presence of a third element $\{C\}$, they are based on statistics.
@@ -10,7 +17,7 @@ They are rules that describes situation where the presence of a given element $\
 - **SUPPORT** --> Fraction of transactions that contain an itemset.
 - **FREQUENT ITEMSET** --> An itemset whose support is greater than or equal to a minsup threshold.
 
-Association rules can be described by the form 
+Association rules can be described by the form
 
 $$
 A \rightarrow C \space where \space A,C \in itemset
@@ -30,21 +37,23 @@ $$
 
 ### CONFIDENCE $conf$
 
-the number of times $C$ appears over transactions that contains $A$ 
+the number of times $C$ appears over transactions that contains $A$
 
 $$
 conf = \frac{(A,C)}{A}
 $$
 
 #### CONFIDENCE FROM SUPPORT
 
-confidence can also be computed from supports as 
+confidence can also be computed from supports as
 
 $$
-conf = \frac{(A,C)}{A} =\frac{\frac{(A,C)}{N}}{\frac{A}{N}} = \frac{sup(A,C)}{sup(A)}  
+conf = \frac{(A,C)}{A} =\frac{\frac{(A,C)}{N}}{\frac{A}{N}} = \frac{sup(A,C)}{sup(A)}
 $$
 
 
 support measures "how much" an occurrence can be considered a rule (there must be enough transaction cases), a rule with low support can be generated by random associations
 
-confidence measures how much a rule is represented in the transactions that contains it  
+confidence measures how much a rule is represented in the transactions that contains it
+
+ [NEXT](ASSOCIATION_RULES_MINING.md)

pages/association_rules/ASSOCIATION RULES MINING.md → pages/association_rules/ASSOCIATION_RULES_MINING.md

@@ -1,14 +1,23 @@
+---
+id: ASSOCIATION RULES MINING
+aliases: []
+tags: []
+index: 2
+---
+
 # ASSOCIATION RULES MINING
 
-The goal of this procedure it's, given a list of $N$ item-set, finding association rules that have  $conf$ and $sup$ grater than some thresholds 
+The goal of this procedure it's, given a list of $N$ item-set, finding association rules that have  $conf$ and $sup$ grater than some thresholds
 
 ## BRUTE-FORCE APPROACH
 
 generate all possible combination and compute $conf$ and $sup$, this approach is always possible but is too much computational expensive
 
 ## TWO STEP APPROACH
 
-this approach is based on the fact that rules that are generated from the same item-set have the same $sup$  
+this approach is based on the fact that rules that are generated from the same item-set have the same $sup$
 
-- **[frequent itemset generation](FREQUENT%20ITEMSET%20GENERATION.md)** -> in the first step all item-set that have $sup \gt threshold$ are generated (**this step is still computational expensive**)
+- **[frequent itemset generation](FREQUENT_ITEMSET_GENERATION.md)** -> in the first step all item-set that have $sup \gt threshold$ are generated (**this step is still computational expensive**)
 - **RULE GENERATION** -> in the second step rules with high confidence are generated from the previous generated item-sets
+
+[PREVIOUS](ASSOCIATION_RULES.md) [NEXT](RULES_GENERATION.md)

pages/association_rules/FP-GROWTH.md

@@ -1,18 +1,25 @@
-The Apriori Alg. needs to generate the candidates sets, whose number can be really high! 
-The FP-Growth algorithm consists on finding shortest patterns to chain with suffixes. 
+---
+id: FP-GROWTH
+aliases: []
+tags: []
+index: 6
+---
+
+The Apriori Alg. needs to generate the candidates sets, whose number can be really high!
+The FP-Growth algorithm consists on finding shortest patterns to chain with suffixes.
 FP-Growth uses a compact representation of the DB via a FP-Tree, on which a recursive approach is used, following the "divide et impera" principle.
 
 ### HOW IT WORKS
 
 1) Data are scanned in order to find the max support for every single item. Non-frequent item are discarded. Frequent items are sorted by decreasing support.
 2) A second scan is done to build the FP-Tree. When the first transaction is read, the A and B nodes are generated with frequency counting = 1.
-					          ![](Pasted%20image%2020231231173158.png)
+					          ![](Pasted_image_20231231173158.png)
 3) When the second transaction is reaa new set containing the B, C and D nodes are created, each one with its relative path starting from the *null* node. Then, the subtree created during step 1) is linked to the just generated one. The two paths do not overlap because of their different prefix.
-							   ![](Pasted%20image%2020231231173623.png)
+							   ![](Pasted_image_20231231173623.png)
 4) If an overlapped path is found (it has the same prefix as a node, let's suppose, A), the counting of the node A is increased by 1.
-						   ![](Pasted%20image%2020231231174113.png) 
+						   ![](Pasted_image_20231231174113.png)
 5) The algorithm continues untill the last transaction.
-						   ![](Pasted%20image%2020231231174157.png)
+						   ![](Pasted_image_20231231174157.png)
 
 The tree size is often lower than the dataset one, but it depends on the transactions orientation.
 
@@ -21,4 +28,11 @@ The tree size is often lower than the dataset one, but it depends on the transac
 Then, FP-Growth procedes with a ***bottom-up *strategy**:
 - The research procedure goes from the less frequent item to the most frequent one. FP-Growth scans the tree in search of itemset ending with the desired search item (es. D).
 - Then look for the only paths that contain the D element. This search is sped up with a pointer data structure.
-- So the subquestion that contains all the itemsets that end in D and that are frequent has to be built. The research is done by evaluating all possible combinations found that include D and that exceed $minSup$ in a divide-and-conquer logic, starting from the leaves to the root.
+- So the subquestion that contains all the itemsets that end in D and that are frequent has to be built. The research is done by evaluating all possible combinations found that include D and that exceed $minSup$ in a divide-and-conquer logic, starting from the leaves to the root.
+
+
+
+
+
+
+[PREVIOUS](APRIORI_ALGORITHM.md)

pages/association_rules/FREQUENT ITEMSET GENERATION.md → pages/association_rules/FREQUENT_ITEMSET_GENERATION.md

@@ -1,3 +1,10 @@
+---
+id: FREQUENT ITEMSET GENERATION
+aliases: []
+tags: []
+index: 4
+---
+
 # FREQUENT ITEM-SET GENERATION
 
 This step  aims to generate all possible  with a $sup \gt threshold$.
@@ -12,22 +19,24 @@ This, approach which have a complexity of $\mathcal{o}(NMW)$ where:
 - $W$ -> average number of items within a transaction
 - $M$ -> number of frequent item-set candidate.
 
-it's extremely computational expensive. 
+it's extremely computational expensive.
 
 There are other strategies that aims to reduce the computational cost of this operation such as:
 
-- reducing the number  of candidates by pruning ([apriori algorithm](APRIORI%20ALGORITHM.md))
+- reducing the number  of candidates by pruning ([apriori algorithm](APRIORI_ALGORITHM.md))
 - reducing the number of comparisons $NM$
 
 ### BRUTE-FORCE APPROACH
 
 The brute-force approach generates each item-set in the graph above. Then, it computes the *sup* and *conf* indexes values for every association rule generated by every item-set.
  - Complexity (**EXPENSIVE**): O(NWM), where
-	 
+
 #### Frequent item-set Generation Strategies
 - Reduce the **number of candidates** M (Apriori Algorithm)
 	- Complete Search: $M=2^D$
 	- Use pruning techniques to reduce M
 - Reduce the **number of comparisons** NM
 	- Use efficient data structures to store the candidates or transactions
-	- No need to match every candidate against every transaction
+	- No need to match every candidate against every transaction
+
+[PREVIOUS](RULES_GENERATION.md) [NEXT](APRIORI_ALGORITHM.md)