👨‍💻 Authors: Scott Chacon & Ben Straub
🏢 Publisher: Apress
📚 Online Git Book: Link

Gaussian Mixture Models (GMM) and EM Algorithm 🎲

● Soft Assignment - we can get a percentage for each group. This is more useful for complex data.
● Flexible Shapes - K-Means only finds circles but GMM can find ellipses (oval shapes) that point in any direction.
● Covariance Types - we can choose different settings for the shape like spherical, diagonal and full.

● These are scores that tell us if the model is good.
● If we add too many groups, the model becomes too complex (Overfitting).
● AIC and BIC give penalties for complexity.

● Every data point starts as its own small cluster.
● The machine finds the two clusters that are closest together.
● The machine joins (merges) them into one new cluster.
● The machine updates the distance between the new cluster and all other clusters.
● It repeats this until all data is in one big cluster.

● Identify the largest vertical gap in the dendrogram (a region with a big jump in height where no merges occur).
● Draw a horizontal line across the dendrogram within this gap.
● Count the number of vertical branches intersected by the line.

● Support - This shows how popular an itemset is in the whole dataset.
 → Support(A) = ((Number of transactions containing A) / (Total number of transactions))

● Confidence - This shows how likely item B is purchased when item A is purchased.
→ Confidence(A → B) = ((Support(A,B)) / (Support(A)))

● Lift -This shows the strength of the rule. If Lift is greater than 1, B is likely to be purchased if A is purchased. If Lift is 1, there is no relationship.
→ Lift(A → B) = ((Support(A,B)) / (Support(A) × Support(B)))

● It only scans the database twice.
● It stores the data in a special tree structure called an FP-Tree.
● After that, the algorithm works mostly with the tree in memory.

Step 1 — Build the FP-Tree
● Removes infrequent items.
● Sorts remaining items by frequency.
● Inserts transactions into tree so shared prefixes overlap.
Step 2 — Mine the Tree (Divide-and-Conquer)
● Starts from the least frequent items
● Builds a Conditional FP-Tree for each item
● Recursively extracts frequent patterns
This is why it is called Frequent Pattern Growth. Patterns grow from smaller conditional structures.

✅ Conviction — Measuring Rule Reliability
Conviction measures how strongly a rule depends on the relationship between A and B by comparing it to a scenario where they are independent.

✅ Leverage — Measuring True Co-Occurrence Gain
Leverage measures how much more often A and B occur together than we would expect if they were independent.

● Point Anomalies (Global Outliers) - A single observation is so far from the other data in the dataset (One data point is abnormal compared to the entire dataset).
Example - a bank account typically showing transactions around $10. But suddenly recording a $1,000,000 of transaction. It immediately stands out.

● Contextual Anomalies (Conditional Outliers) - A data point is normal in a general context. but becomes anomalous when studied within a specific context like time, location or user behaviour.
Example - 30°C is normal during the summer season but the same temperature is highly unusual in winter (same value, but provides completely different ideas based on the context).

● Collective Anomalies - in this, individual data points look normal but a sequence or group of those same data points sometimes shows an unusual pattern.
Example - One failed login attempt is normal but hundreds of failed logins within seconds are highly suspicious.

● K-Distance - For each point, compute the distance to its kth nearest neighbor.
● Local Reachability Density (LRD) - Now we estimate how crowded the area is.
● Compute the LOF Score - It compares the LRD of a point to the LRD of its neighbours.

● Precision-Recall Curve - To see how many true anomalies we detect vs false alarms.
● F1-Score - The balance between finding all anomalies and not being too sensitive. F1 score combines precision and recall into a single number.

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Bootstrapping - the machine creates multiple subsets of the original data. It does this by sampling with replacement. This means some data points appear multiple times in one subset while others do not appear at all.
Parallel Training - we train a separate model (usually a Decision Tree) on each subset simultaneously. Aggregating - to make a final prediction, machine combines the results of all models. For Classification, It uses majority voting. For Regression, It uses the average of all predictions.

The Math & Logic,

In a normal Decision Tree, the machine looks at all features to find the best split. In a Random Forest, for every split, the machine only looks at a random subset of features. This prevents one very strong feature from dominating every tree. It forces the trees to be different. It makes the final forest much more stable and accurate.

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