vault backup: 2024-10-03 00:52:44

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Biometric Systems/final notes/2. Performance indexes.md

@@ -39,37 +39,33 @@ Most difficult traits to exploit:
 - Euclidian distance
 - Cosine similarity
 	- cosine of the angle between two vectors
-- Pearson correlation
-- Bhattacharyya distance
-
-
-> [!PDF|yellow] [[LEZIONE2_Indici_di_prestazione.pdf#page=9&selection=8,0,10,31&color=yellow|LEZIONE2_Indici_di_prestazione, p.9]]
-> > or cosine similarity may provide either a distance measure or a similarity measure
-> 
-> shows "more stuff" than Euclidian distance, such as orientation ecc.. Shows how templates are similar to eachother. While distance shows how templates are... distant!
+	- affected also by the direction of the vectors
+- Pearson correlation (for histograms or sets of points)
+	- statistical measure that evaluates the **linear relationship** between two variables. It tells you whether an increase or decrease in one variable tends to correspond with an increase or decrease in another, and how strong that relationship is (ChatGPT)
+- Bhattacharyya distance (histograms)
+	- measure of the similarity (or dissimilarity) between two probability distributions
+	- the Bhattacharyya distance can compare feature distributions between two different classes (e.g., color histograms of objects)
 
 > [!PDF|yellow] [[LEZIONE2_Indici_di_prestazione.pdf#page=10&selection=3,1,4,21&color=yellow|LEZIONE2_Indici_di_prestazione, p.10]]
 > > (Pearson) Correlation
 > 
 > how signals are similar to eachother. Often used to compare fingerprints, by computing the correlation between two fingerprints.
 
-Histograms needs other ways to be compared.
+For time series we have to address an issue: temporal sequences may vary in speed or timing, e.g. in two repetitions of a walking sequence, there might be differences in walking speed between repetitions, but the spatial path of limbs remain highly similar.
+Another example could be audio recordings, same voice but different speed.
 
-The same happens with time series: speed for example may speed the final outcome of the time series, even if the patterns are the same.
+Dynamic Time Warping allows for "warping" of the time axis, meaning it can stretch or compress sections of the sequences to achieve the best possible alignment. This is useful when parts of one sequence are faster or slower than the corresponding parts in the other sequence.
 
-So what do we do?
-sometimes we use correlation, but Dynamic time Warping is the most used.
 
 ![[Pasted image 20241002135922.png]]
 
-each point is paired with the most convenient one. It's not necessaty that points corresponds to the same instant in time.
+each point is paired with the most convenient one. It's not necessarily that points corresponds to the same instant in time.
 
-if using deep learning we should use the architecture to extract the embeddings (for both gallery and probe templates).
+##### Comparing the results of submitting a template to a Deep Learning model
+- if using deep learning we should use the architecture to extract the embeddings (for both gallery and probe templates): we can delete the classification layer in order to get the embeddings that the architecture would use for the final classification.
+- mbeddings can be compard as they were vectors of hand-crafted features.
 
-//
-after normalization in range [0, 1] we will have that distance = 1 - similarity.
-
-#### Possible errors: verification
+### Possible errors: verification
 - Genuine Match (GM, GA): the claimed identity is true and subject is accepted
 - False Rejection (FR, FNM, type I error): claimed identity is true but the subjet is rejected
 - Genuine Reject (GR, GNM): an impostor is rejected
@@ -79,13 +75,18 @@ It's important to define a good threshold.
 If too high we will get a lot of false acceptance. If too low we will get a lot of false rejection!
 
 When computing rates:
-- False Rejection Rate (FRR) is the number of FR divided by ONLY the number of GM+FR.
-	- in fact, GM + FR have the same denominator and sum up to 1.
-- False Acceptance Rate is the number of FA divided by FA + GR
+- **False Rejection Rate (FRR)** is the number of FR divided by the number of GM+FR.
+	- in fact, GM and FR have the same denominator and sum up to 1.
+- **False Acceptance Rate** is the number of FA divided by total number of impostor attempts (FA + GR)
+- **Equal Error Rate** is the value at a specific threshold, where FAR and FRR are the same value.
+- **Detection Error Trade-off:** a plot that shows the **trade-off** between the **FAR** and **FRR** at different threshold settings of a system
+- **Receiving Operating Curve:** a plot that shows the True Positive Rate (TPR) (also called **Sensitivity**) against the False Positive Rate (FPR) (1 - Specificity) at various threshold settings.
 
-Equal Error Rate is the value at a specific threshold, where FAR and FRR are the same value.
+Key Differences Between ROC and DET Curves:
+- **ROC Curve**: Focuses on the **true positives** and **false positives**, showing the ability to discriminate between classes (genuine vs impostor).
+- **DET Curve**: Focuses on the **false rejection rate (FRR)** and **false acceptance rate (FAR)**, helping to analyze trade-offs between security and usability in verification systems.
 
-two synthetic metrics could be ERR and area below ROC curve.
+Two synthetic metrics for instance could be ERR and area below ROC curve.
 
 (we might have more templates for the same person to address inter-class variation.
 Of course templates should be different, not computed i.e. by frames of the same video, as some of them could be blurred and close frames are exactly the same!)