Lec-14: Hierarchical Clustering | Agglomerative vs Divisive with examples

1. Audio
   Observation

   Says: Let's take a small dataset and count in order: 1, 5, 8, 10, 19, 20.

2. Diagram
   Observation

   Six numbers—1, 5, 8, 10, 19, 20—are written on the bottom row of the whiteboard.

\{1,5,8,10,19,20\}

For example, a one-dimensional dataset is taken; each number is a separate data point.

Initially, each element is itself a cluster.

1. Audio
   Observation

   Says: First, we construct the proximity matrix, and from it, we determine the pairwise differences.

2. Diagram
   Observation

   In the top-right corner, a partial matrix for 1, 5, 8 is written: first row 0, 4, 7; second row 4, 0, 3; third row 7, 3, 6.

1. The full $6\times 6$ matrix is not shown; only a partial view of the portion involving 1, 5, 8 appears.

P

Proximity matrix—that is, a table holding the pairwise distances between data points.

In this video, distance is explained as the absolute difference between numbers.

1. Audio
   Observation

   Says: The pair with the smallest distance is grouped into one cluster, so 19 and 20 form a cluster.

2. Diagram
   Observation

   A bracket is drawn above 19 and 20, and (19,20) is written there.

(19,20)

The first merged cluster formed from 19 and 20.

After merging, this is a group of two original points.

1. Audio
   Observation

   Says that I have created another cluster from 8 and 10.

2. Diagram
   Observation

   A bracket is drawn over 8 and 10, written as (8,10).

(8,10)

The second merged cluster formed from 8 and 10.

After merging, this is a group of two original points.

1. Audio
   Observation

   Says that initially there were six items total; now only four remain.

2. Diagram
   Observation

   After clustering, the remaining units present on the board are 1, 5, (8,10), and (19,20).

$6 \to 4$

After two merge operations, the number of independent units decreased from 6 to 4.

This count illustrates the decrease in cluster count during the agglomerative process.

1. Diagram
   Observation

   The whiteboard continuously displays the title "Hierarchical clustering" and the bullet points "Agglomerative & Divisive".

$\text{Hierarchical clustering}$

The topic name covered in this segment: hierarchical clustering.

$\text{Whiteboard title, used throughout the entire segment}$

1. Diagram
   Observation

   Below the title is written "Agglomerative & Divisive".

2. Audio
   Observation

   After 00:00:59, the instructor explicitly labels the left-hand process as agglomerative and the right-hand process as divisive.

$\text{Agglomerative \& Divisive}$

Two opposite construction approaches for hierarchical clustering: bottom-up merging or top-down splitting.

$\text{Whiteboard subtitle}$

1. Diagram
   Observation

   At the bottom of the dendrogram in the lower-left corner, data points 1, 5, 8, 10, 19, and 20 are visible.

2. Diagram
   Observation

   In the upper-right corner, there is also a handwritten matrix-like numeric array, but it is not used in subsequent derivations within this segment.

1. The matrix in the upper-right corner is not verbally explained in this segment; its purpose remains to be verified.

1,5,8,10,19,20

Six observations from the example dataset, used to demonstrate the hierarchical clustering dendrogram.

$\text{Example set of data points}$

1. Diagram
   Observation

   The left side already has parentheses labeled (8,10), indicating that 8 and 10 have already been merged into a single cluster.

2. Audio
   Observation

   The instructor says, 'in which 8 and 10 were already there earlier', confirming that this cluster previously existed.

(8,10)

The initial subcluster formed by points 8 and 10.

Intermediate clusters during the agglomerative process

1. Diagram
   Observation

   Another branch on the left labeled (19,20).

2. Audio
   Observation

   During the final merge, the instructor says, 'Which second cluster has arrived—the one with 19 and 20?'

(19,20)

Another subcluster formed by points 19 and 20.

Intermediate clusters during the agglomerative process

1. Diagram
   Observation

   The instructor writes (8, 10) above (5, (8, 10)).

2. Audio
   Observation

   The instructor says, '5 and 8 have been combined in this way', then describes it as a larger cluster.

1. The verbal description mentions 5 and 8, but the actual merging shown on the board is between 5 and the cluster (8,10).

(5,(8,10))

The new cluster formed by incorporating point 5 into the existing cluster (8,10).

Intermediate clusters during the agglomerative process

1. Diagram
   Observation

   The instructor continues upward, writing (1,(5,(8,10))).

2. Audio
   Observation

   The instructor says "1 and all of these" and calls it a new cluster.

(1,(5,(8,10)))

The larger cluster formed by incorporating point 1 into the cluster (5,(8,10)).

Intermediate clusters during the agglomerative process

1. Audio
   Observation

   The instructor says this section will explain hierarchical clustering and first reviews ordinary clustering: grouping similar, mutually proximate data points into the same cluster, and assigning non-proximate points to different clusters.

2. Audio
   Observation

   The instructor then explains the meaning of hierarchy: attaching layer by layer, like a sequence, and draws an analogy to inheritance—grandparents → parents → child.

3. Diagram
   Observation

   The slide title reads "Hierarchical clustering", with bullet points below reading "Agglomerative & Divisive".

The video first defines ordinary clustering as grouping similar and mutually proximate data points into the same cluster, and dissimilar points into different clusters. It then interprets "hierarchy" as a serialized, layer-by-layer relational structure—not merely a one-time flat grouping. The instructor uses a family inheritance chain as an analogy, emphasizing that clusters themselves can further form hierarchical, parent-child relationships.

1. The subject under discussion is the similarity among data points and their grouping relationships.

2. Here, "hierarchy" refers to the possibility of organizing clusters themselves in a layered fashion.

1. Audio
   Observation

   The instructor begins from a business point of view, giving an example: an e-commerce website has many consumers or customers, who predominantly purchase clothes, electronics, or groceries, respectively.

2. Audio
   Observation

   The instructor criticizes the blanket discount "सबको 50% off" for lacking a target audience and thus having limited effectiveness.

3. Audio
   Observation

   The instructor proposes a better approach: first build clusters based on purchasing preferences, then construct a hierarchy, and offer different discount percentages to different groups.

The video uses the e-commerce scenario to illustrate why hierarchical clustering is needed: applying a uniform discount to all customers lacks targeting; instead, if customers are first grouped into clusters based on purchasing behavior, and those clusters are further subdivided internally, tailored promotions can be designed for different groups. The core emphasis here is not a single clustering result, but rather the organizational method governing relationships among clusters.

1. The example scenario is e-commerce customer segmentation.

2. The goal is to form more targeted audience groups.

1. Intuitive definition of hierarchical clustering

1. Audio
   Observation

   The instructor says, "So here you can create them in two ways: one agglomerative and one divisive."

2. Diagram
   Observation

   The slide bullet points explicitly state "Agglomerative & Divisive".

3. Audio
   Observation

   The instructor further explains, "Agglomerative means aggregation," and says all data points are initially separate; then begins explaining what basis to use for aggregation, but the sentence remains incomplete before the clip ends.

1. The instructor's full definition of agglomerative is cut off at 120 seconds; subsequent specific algorithmic steps do not appear in this clip.

At the end of this clip, the video formally introduces the two construction approaches of hierarchical clustering: agglomerative and divisive. The instructor verbally links agglomerative with aggregation, suggesting the idea of gradually grouping originally separate data points; although divisive is named, its definition is not elaborated within this clip.

1. Two construction paths belonging to hierarchical clustering.

2. This clip only completes naming and initial prompting, without presenting the full algorithmic procedure.

1. Intuitive definition of hierarchical clustering

1. Caption evidence
   Observation

   The title reads 'Hierarchical clustering'.

2. Caption evidence
   Observation

   The bullet point reads 'Agglomerative & Divisive'.

3. Audio
   Observation

   The presenter describes both types as bottom-up and top-down, respectively.

In this section, hierarchical clustering is divided into two approaches: agglomerative, also called the aggregation or bottom-up approach, and divisive, also called the division-based or top-down approach. In agglomerative clustering, all individual points are combined one by one based on their closeness. In divisive clustering, all points start together and are then further divided.

1. The video provides only a conceptual introduction.

2. No formal algorithm or linkage criterion is explained in this section.

1. Audio
   Observation

   The speaker says we first create a proximity matrix.

2. Audio
   Observation

   The speaker says we identify differences among points through that matrix.

3. Diagram
   Observation

   A partial distance table is written for 1, 5, and 8.

1. The full $6\times 6$ table is not drawn on the board.

The proximity matrix is the table in which the pairwise differences or distances between data points are recorded. In the example, 1 and 1 between 0, 1 and 5 between 4, 1 and 8 between 7, 5 and 5 between 0, and 5 and 8 between 3 is written. The instructor says we can also use the Euclidean distance formula and there are various methods.

1. Here the example is based on one-dimensional numerical data.

2. The video presents several distance options, but no formal derivation is given.

1. Two types of hierarchical clustering

1. Audio
   Observation

   Says that those with the smallest distance are placed into one cluster.

2. Diagram
   Observation

   First, clusters (19,20) and then (8,10) are formed.

3. Audio
   Observation

   Says that initially there were six items total, now four remain.

1. How the new cluster-to-cluster distances will be updated is not explained in this section.

In this section, agglomerative clustering is explained as follows: initially, all points are treated as separate; then, the pair with the smallest distance is merged into one cluster. In the example, the distance between 19 and 20 is 1, so they merge first; afterward, the distance between 8 and 10 is 2, so they merge. With each merge, the number of independent units decreases.

1. Initially, each data point is its own cluster.

2. The choice of merge is based on the pair with the minimum distance.

3. In this section, the linkage rule is not explained in detail.

1. Proximity matrix

1. Diagram
   Observation

   The whiteboard title reads "Hierarchical clustering".

2. Audio
   Observation

   After 00:00:59, the instructor concludes that a "hierarchy of clustering" can be created in this way.

This segment interprets hierarchical clustering as a method of progressively organizing data points into nested clusters: either by repeatedly merging individual points, or by repeatedly splitting the entire set, ultimately forming a tree-like hierarchical structure.

1. a dataset where distances or similarities can be compared

2. the video demonstrates with six one-dimensional example points

1. Audio
   Observation

   the instructor repeatedly uses the word "combine" to describe merging two objects into a single cluster

2. Diagram
   Observation

   the left tree merges upward layer by layer from the bottom points 1,5,8,10,19,20 to the root node

3. Audio
   Observation

   at approximately 00:01:04, the instructor explicitly says "just like I did in agglomerative because I went from bottom to up"

the agglomerative approach starts from individual samples and progressively merges clusters according to their current nearest relationships until all samples belong to a single root cluster. the video illustrates this process using (8,10) → (5,(8,10)) → (1,(5,(8,10))) → ((1,(5,(8,10))),(19,20))

1. bottom-up construction

2. at each step, two existing objects or clusters are merged into a larger cluster

1. Hierarchical clustering

1. Diagram
   Observation

   the right side starts from (1,5,8,10,19,20) and splits downward into (1,5,8,10) and (19,20), then continues splitting

2. Audio
   Observation

   the instructor says "if you do divisive ... first ... it is separate ... then after that ... it is split"

3. Audio
   Observation

   at approximately 00:01:34, the instructor summarizes "in a sense, you go top to down here, and bottom to up there"

The divisive method starts with one large cluster containing all samples and progressively splits clusters into smaller subclusters until reaching individual samples. The right side of the video demonstrates that (1,5,8,10,19,20) is first split into (1,5,8,10) and (19,20), then the former is further split into 1 and (5,8,10), then into 5 and (8,10), and finally into 8 and 10.

1. Top-down construction

2. At each step, one existing cluster is split into several smaller clusters

1. Hierarchical clustering

1. Diagram
   Observation

   The instructor writes "Dendrogram" beside the tree on the left.

2. Audio
   Observation

   The instructor says "We call this a dendrogram ... like a line chart, a graph chart ... a histogram — you have this kind of chart called a dendrogram."

The video refers to the tree-like structure resulting from hierarchical clustering as a dendrogram. It uses branches and nodes to represent the nested relationships among clusters, visualizing the merging or splitting process.

1. Tree-like structure used to represent hierarchical clustering

1. Hierarchical clustering
2. agglomerative hierarchical clustering
3. Divisive hierarchical clustering

1. Audio
   Observation

   The instructor says "There is a scipy library inside Python, within which you can create this."

1. The video does not provide specific function names or code examples.

The instructor adds that the scipy library in Python can be used to build such hierarchical clustering structures. This is only a tool tip, with no implementation details provided.

1. Used in a Python environment

2. The video does not show the specific API calls.

1. Dendrogram

1. Audio
   Observation

   Says that agglomerative clustering proceeds from bottom to top because all points are separate at the bottom.

2. Audio
   Observation

   Says that divisive means division-based and follows a top-down approach.

Agglomerative clustering is bottom-up: separate points are merged based on closeness. Divisive clustering is top-down: all points start in one cluster and are then divided.

1. The video provides a comparative introduction to both methods.

All illustrative cases presented by the speaker.

1. Audio
   Observation

   Says that the pair with the smallest distance is placed into one cluster.

2. Diagram
   Observation

   19 and 20 are placed into one cluster first.

1. This rule is explained in this section through examples, not proven as a formal theorem.

In this example, the next choice in agglomerative clustering is made on the pair with the smallest distance; therefore, 19 and 20 merge first.

1. Pairwise distances are available nearby.

2. The basis for merging is the minimum distance.

Over all candidate pairs at the current step in the example.

1. Audio
   Observation

   The instructor says, 'Like in agglomerative, I did it because I went from bottom to up.'

2. Diagram
   Observation

   The left tree indeed merges upward from individual points at the bottom to the root.

Agglomerative hierarchical clustering starts from individual samples and progressively merges upward to form larger clusters.

1. Using the agglomerative construction method shown in the video

$\forall \text{Merging step in this example}$

1. Audio
   Observation

   When referring to divisive, the instructor says it first starts from the entire set and then repeatedly 'splits it apart'.

2. Audio
   Observation

   The instructor summarizes, 'In one sense, you go top to down here, and bottom to up there.'

3. Diagram
   Observation

   The right tree splits downward from the top-level full set.

Divisive hierarchical clustering starts with a single cluster containing all samples and progressively splits it into smaller clusters.

1. Using the divisive construction shown in the video.

$\forall \text{Splitting step in this example}$

1. Diagram
   Observation

   The left agglomerative tree and the right divisive tree contain the same leaf points and the same nested groupings.

2. Audio
   Observation

   The instructor presents both methods side by side and demonstrates them using the same dataset 1,5,8,10,19,20.

1. This summary is derived by comparing the contents of the two trees; the video does not state it as a formal theorem.

For the same dataset in this example, agglomerative and divisive approaches can produce tree structures that are opposite in direction but identical in hierarchical content.

1. Using the same set of data points.

2. Adopting the same nested groupings shown in the video.

$\exists \text{Same dataset in this example}$

1. Audio
   Observation

   The speaker computes distances: 4, 3, 2, 9, 1.

2. Diagram
   Observation

   Clusters are formed from (19,20) and (8,10).

3. Audio
   Observation

   States that there were initially six items, and now four remain.

1. The full updated proximity matrix is not shown after the merge.

1. Expression

   $$\{1,5,8,10,19,20\}$$
   Explanation

   The initial dataset consists of six distinct points.

   Justification

   The instructor wrote these numbers on the board and stated that they are distinct data points.

   Shown in the video
2. Expression

   $$d(19,20)=1$$
   Explanation

   The distance between 19 and 20 is 1.

   Justification

   This arises from the numerical difference, and the instructor identified it as the smallest distance.

   Shown in the video
3. Expression

   $$(19,20)$$
   Explanation

   The first cluster is formed by merging the pair with the smallest distance.

   Justification

   The instructor stated that the pair with the smallest distance is placed into one cluster.

   Shown in the video
4. Expression

   $$d(8,10)=2$$
   Explanation

   The distance between 8 and 10 is 2.

   Justification

   The instructor identified the next smallest distance as 2 and merged that pair.

   Shown in the video
5. Expression

   $$(8,10)$$
   Explanation

   A second cluster is formed by merging 8 and 10.

   Justification

   This follows an agglomerative merge step.

   Shown in the video
6. Expression

   $$\{1,5,(8,10),(19,20)\}$$
   Explanation

   After two merges, four independent units remain.

   Justification

   The instructor explicitly stated that there were initially six total items, and now four remain.

   Shown in the video

In this example, agglomerative clustering proceeds by merging the pair with the smallest distance, and the cluster/unit count decreases with each merge.

1. Audio
   Observation

   The instructor sequentially explains merging 5 into (8,10), then merging 1 in, and finally merging the two large clusters.

2. Diagram
   Observation

   The board writing step by step shows (5,(8,10)), (1,(5,(8,10))), and ((1,(5,(8,10))),(19,20)).

1. Expression

   $$(8,10)$$
   Explanation

   The process starts with pre-existing subclusters: point 8 and point 10 are first grouped together.

   Justification

   This cluster is already displayed on the board at the beginning of the video, and the instructor also states that it previously existed.

   Shown in the video
2. Expression

   $$(5,(8,10))$$
   Explanation

   Merge point 5 with cluster (8,10) to form a larger cluster.

   Justification

   The instructor says '5 and 8 are combined in this way' and writes the nested form on the board.

   Shown in the video
3. Expression

   $$(1,(5,(8,10)))$$
   Explanation

   Then merge point 1 into the cluster obtained in the previous round.

   Justification

   The instructor says 'a cluster of 1 and all these has been created'.

   Shown in the video
4. Expression

   $$((1,(5,(8,10))),(19,20))$$
   Explanation

   Finally merge the left large cluster with the right cluster (19,20) to form the root cluster.

   Justification

   The instructor says that only two clusters remain at this point, so they are combined into a single item.

   Shown in the video

Through successive merging, six points are organized into a bottom-up hierarchical clustering tree.

1. Diagram
   Observation

   On the right, splitting starts downward from (1,5,8,10,19,20).

2. Audio
   Observation

   The instructor explains step by step: first split off (19,20), then split off 1, then split off 5, and finally split off 8 and 10.

1. Expression

   $$(1,5,8,10,19,20)$$
   Explanation

   Start with a single large cluster containing all samples.

   Justification

   At the top of the right-hand board, the universal set is written; the instructor says divisive begins with 'all of these, all of these'.

   Shown in the video
2. Expression

   $$(1,5,8,10) \quad (19,20)$$
   Explanation

   The first split divides the universal set into two subclusters.

   Justification

   The instructor says '19 and 20 form one separate group, and 1, 5, 8, 10 form another separate group.'

   Shown in the video
3. Expression

   $$1 \quad (5,8,10)$$
   Explanation

   Then split (1,5,8,10) into the singleton 1 and the remaining cluster.

   Justification

   The instructor says 'Then we separated 1, and made a separate group for 5, 8, 10.'

   Shown in the video
4. Expression

   $$5 \quad (8,10)$$
   Explanation

   Continue splitting (5,8,10) into 5 and (8,10).

   Justification

   The instructor says 'Then we separated 5, and made a separate group for 8 and 10.'

   Shown in the video
5. Expression

   $$8 \quad 10$$
   Explanation

   Finally, split (8,10) into two singletons.

   Justification

   The instructor says, “Then you have separated 8 and 10.”

   Shown in the video

Through successive splitting, the initial full set is reduced to individual samples, forming a top-down hierarchical clustering tree.

1. Audio
   Observation

   The instructor gives an example of an e-commerce website, mentioning that customers tend to buy clothes, electronics, or groceries more frequently.

2. Audio
   Observation

   The instructor compares two strategies: one is "everyone gets 50% off," and the other is first clustering customers by purchasing preference, then offering different discounts to different clusters.

Suppose you run an e-commerce website with many consumers, whose purchasing preferences are concentrated respectively on clothes, electronics, and groceries. How can promotions be designed more effectively than applying a uniform fifty percent discount to everyone?

1. There exist many customers or consumers

2. Different customers have different consumption tendencies toward clothes, electronics, and grocery

3. The goal is to design more targeted discounts based on behavioral differences

Explain how hierarchical grouping yields more targeted audiences.

1. Expression

   $$$$
   Explanation

   First, divide the entire population into different clusters according to customers' consumption preferences—for example, groups preferring clothes more, electronics more, or groceries more.

   Justification

   This is a direct application of ordinary clustering shown in the video: grouping people with similar behaviors together.

   Shown in the video
2. Expression

   $$$$
   Explanation

   Build a hierarchy on top of these clusters so that different groups correspond to different discount rates.

   Justification

   The video emphasizes that the role of hierarchy is to establish relationships among clusters, not merely to perform one-time grouping.

   Shown in the video
3. Expression

   $$$$
   Explanation

   Offer clothing discounts primarily to the group with stronger clothing preference, and offer another set of discounts to the electronics-preference group.

   Justification

   The instructor explicitly states that only this approach aligns with the patterns and trends of different populations.

   Shown in the video

The video's conclusion is: clustering first, then performing hierarchical subdivision, is more effective at forming a targeted audience than offering everyone a uniform 50% discount.

This example involves no numerical computation; the verification method is to check whether it reflects the two points repeatedly emphasized in the video: similar objects belong to the same cluster, and clusters themselves can further form hierarchical relationships.

1. Audio
   Observation

   The instructor says, "I’ll explain using a simple example."

2. Diagram
   Observation

   1, 5, 8, 10, 19, and 20 are written on the board, and then clusters are formed.

1. The full proximity matrix and all subsequent merge steps are not shown in this segment.

Data points 1, 5, 8, 10, 19, and 20 are given; we begin clustering them agglomeratively based on distance.

1. The dataset is \{1,5,8,10,19,20\}.

2. Initially, each point is its own cluster.

3. In the example for distance, the difference between numbers is used.

4. The presenter identified constructing the proximity matrix as the first step.

Show the first few agglomerative merge steps by combining pairs with smaller distances.

1. Expression

   $$P \text{ बनाएँ}$$
   Explanation

   First, construct the pairwise differences of the data points / the proximity matrix.

   Justification

   The presenter said we create the proximity matrix first.

   Shown in the video
2. Expression

   $$d(19,20)=1$$
   Explanation

   Among all displayed distances, the difference between 19 and 20 is the smallest.

   Justification

   The presenter stated that distance 1 is the smallest.

   Shown in the video
3. Expression

   $$(19,20)$$
   Explanation

   19 and 20 are merged into one cluster.

   Justification

   The rule of merging the pair with the minimum distance applies here.

   Shown in the video
4. Expression

   $$d(8,10)=2$$
   Explanation

   The next smallest distance 8 and 10 between 2 is.

   Justification

   The presenter indicated the next merge by selecting distance 2.

   Shown in the video
5. Expression

   $$(8,10)$$
   Explanation

   8 and 10 are merged to form the second cluster.

   Justification

   This is the next step of the same agglomerative procedure.

   Shown in the video
6. Expression

   $$\{1,5,(8,10),(19,20)\}$$
   Explanation

   After these two merges, four units remain.

   Justification

   The narrator stated while counting that six items were reduced to four.

   Shown in the video

After the displayed steps, the clusters are \{1,5,(8,10),(19,20)\}.

In the example, the merge choice is made according to the order of distances: 19-20 for 1, then 8-10 for 2; and unit count 6 from 4 down to shown.

1. Diagram
   Observation

   Both the left and right trees use the same set of bottom data points: 1, 5, 8, 10, 19, 20.

2. Audio
   Observation

   The instructor fully demonstrates both agglomerative and divisive processes using these six points.

Given data points 1, 5, 8, 10, 19, 20, demonstrate how to form a tree structure using hierarchical clustering, and compare the agglomerative and divisive approaches.

1. The data points are 1, 5, 8, 10, 19, 20

2. On the left, the subclusters (8, 10) and (19, 20) are already given.

3. The video uses tree-like connections to represent merging or splitting relationships.

Construct the complete hierarchical clustering tree and explain the differences between the two methods.

1. Expression

   $$(8,10),\ (19,20)$$
   Explanation

   First, acknowledge the two existing subclusters.

   Justification

   At the start of the video, the left blackboard already shows these two groups.

   Shown in the video
2. Expression

   $$(5,(8,10))$$
   Explanation

   In the agglomerative side, merge 5 into (8,10).

   Justification

   The instructor explains orally and writes on the board.

   Shown in the video
3. Expression

   $$(1,(5,(8,10)))$$
   Explanation

   Then merge 1 again.

   Justification

   The instructor continues constructing new clusters upward.

   Shown in the video
4. Expression

   $$((1,(5,(8,10))),(19,20))$$
   Explanation

   Finally, merge the two main branches into the root.

   Justification

   The instructor says the final combine occurs when only two clusters remain.

   Shown in the video
5. Expression

   $$(1,5,8,10,19,20) \to (1,5,8,10),(19,20) \to 1,(5,8,10) \to 5,(8,10) \to 8,10$$
   Explanation

   On the right side, perform divisive reverse splitting using the same intuitive level.

   Justification

   After writing 00:01:08, the instructor writes and states the splitting order step by step.

   Shown in the video

The left side yields a bottom-up agglomerative tree; the right side yields a top-down divisive tree; both represent the same nested cluster relationships.

Verification can be done by checking whether the leaf sets and intermediate clusters match between the two trees; in the video, both trees use the same grouping level.

1. Diagram
   Observation

   The entire segment's background is a light-blue-to-white gradient slide, with the title 'Hierarchical clustering' in the top-left corner, followed by a bulleted line reading 'Agglomerative & Divisive'.

2. Diagram
   Observation

   A whiteboard software toolbar is visible at the bottom, and the page number displayed on the right reads '$3/4$'.

1. Title 'Hierarchical clustering'

2. Bullet point 'Agglomerative & Divisive'

3. Instructor

4. Bottom toolbar

5. Page number $3/4$

1. The instructor continuously gestures while explaining on camera.

2. The slide text itself remains unchanged

1. The page theme is always hierarchical clustering

2. The terms 'agglomerative' and 'divisive' are always visible on screen

This slide serves as a course topic prompt: it first gives the main title, then reveals the names of the two hierarchical clustering approaches in advance, providing anchor points for the upcoming verbal explanation.

1. Caption evidence
   Observation

   The title 'Hierarchical clustering' and the bullet 'Agglomerative & Divisive' appear consecutively.

2. Animation
   Observation

   The narrator makes gestures with hands moving up and down, and separating or joining.

1. Title 'Hierarchical clustering'

2. Bullet 'Agglomerative & Divisive'

3. The narrator's facial expressions

1. The narrator first verbally links and then distinguishes both types.

2. Gestures indicate the bottom-up and top-down directions.

1. The title and bullet text remain unchanged.

This scene explains the contrasting flows of agglomerative and divisive methods using physical cues.

1. Diagram
   Observation

   The presenter writes 1, 5, 8, 10, 19, 20 on the bottom row.

1. The numbers 1, 5, 8, 10, 19, 20.

1. Six distinct data points are written in sequence.

1. All of these are initially independent points.

This shows the initial state of the agglomerative procedure, where each point is its own cluster.

1. Diagram
   Observation

   A partial matrix for 1, 5, 8 is written in the upper right: 0, 4, $7 / 4$, 0, $3 / 7$, 3, 6.

1. The full $6\times 6$ matrix is not constructed; only a partial portion appears.

1. Row/column labels 1, 5, 8

2. Entries 0, 4, 7, 3, 6

1. Pairwise differences are filled in as a table.

1. The narrator's goal is to compute distance, not to merge yet.

This step represents distance computation in agglomerative clustering.

1. Diagram
   Observation

   A bracket is drawn above 19 and 20, and (19,20) is written.

1. 19

2. 20

3. (19,20)

1. Two distinct points combine to form one cluster.

1. Other points remain untouched.

This is the direct visual step of merging the pair with the minimum distance.

1. Diagram
   Observation

   A bracket is placed above 8 and 10, written as (8,10).

1. 8

2. 10

3. (8,10)

1. Another pair merges to form the second cluster.

1. 1 and 5 remain separate points.

This shows that the agglomerative process successively reduces the cluster count.

1. Audio
   Observation

   The instructor says there were initially six total items, and now four remain.

2. Diagram
   Observation

   On the board, the positions of 1, 5, (8,10), and (19,20) are shown.

1. 1

2. 5

3. (8,10)

4. (19,20)

1. The count of independent units decreases after two merges.

1. The total number of original data points remains the same; only the grouping changes.

This illustrates the sequential reduction property of agglomerative clustering.

1. Diagram
   Observation

   Building upon existing (8,10) and (19,20) on the left, the instructor draws connecting lines upward and adds cluster labels.

2. Animation
   Observation

   The writing order proceeds from lower-level clusters gradually toward higher-level root nodes.

1. Data points at the bottom: 1, 5, 8, 10, 19, 20

2. Subclusters (8, 10) and (19, 20)

3. New clusters: (5, (8, 10)), (1, (5, (8, 10))), and the root cluster ((1, (5, (8, 10))), (19, 20))

1. First, add 5 to (8, 10)

2. Then, add 1 to the new cluster

3. Finally, connect the two large left and right branches to a common root node

1. The set of leaf nodes is always 1, 5, 8, 10, 19, 20

2. The internal members of existing subclusters (8, 10) and (19, 20) remain unchanged

The animation uses an upward-growing tree to indicate the 'merging' direction: each level contains more samples than the level below it.

1. Diagram
   Observation

   On the right, splitting begins from the top (1, 5, 8, 10, 19, 20) and proceeds downward.

2. Animation
   Observation

   The instructor writes subclusters sequentially and extends branches downward.

1. The top-level universal set (1,5,8,10,19,20)

2. Subclusters (1,5,8,10) and (19,20)

3. Subsequent subclusters 1, (5,8,10), 5, (8,10), 8, 10

1. First split the universal set into two branches

2. Then recursively split larger clusters into smaller ones layer by layer

3. Eventually reaching individual samples

1. All branches together still cover the original six points

2. Splitting does not introduce new data points

The animation uses downward branching to indicate the direction of 'splitting': each level is finer than the one above it.

1. Diagram
   Observation

   The instructor writes 'Dendrogram' beside the tree on the left.

1. Left-side hierarchical clustering tree

2. Handwritten label: dendrogram

1. Shifting from simply drawing a figure to naming the figure

1. The tree structure itself remains unchanged

This step formally defines the previously drawn hierarchical tree as a dendrogram.

1. Diagram
   Observation

   The whiteboard displays the title 'Hierarchical clustering' and the subtitle '• Agglomerative & Divisive'. On the left is a dendrogram with leaf nodes labeled 1, 5, 8, 10, 19, and 20 at the bottom; on the right is another hierarchical tree structure, with the set (1,5,8,10,19,20) visible near the top, and lower branches including (1,5,8,10), (19,20), (5,8,10), and (8,10), among others.

2. Animation
   Observation

   The whiteboard content remains largely static throughout the clip; the instructor stands in front of it and gestures, with no new writing, erasing, or graphical changes observed.

1. Some node labels in the left dendrogram are unclear; only the bottom numbers and several parenthesized groupings can be reliably transcribed.

2. The full hierarchical relationships of the right-hand tree structure are not verbally explained within 6 seconds; only the visible nodes can be recorded, and its construction rules cannot be inferred.

1. Title: Hierarchical clustering

2. Subtitle: Agglomerative & Divisive

3. Left dendrogram

4. Right hierarchical clustering structure

5. Leaf node numbers 1, 5, 8, 10, 19, 20

6. Parenthesized groupings such as (19,20), (8,10), (5,8,10), (1,5,8,10), and (1,5,8,10,19,20)

1. The instructor moves in front of the board and gestures.

2. The diagram and text on the whiteboard show no visible change.

1. The title 'Hierarchical clustering' remains visible throughout.

2. The subtitle 'Agglomerative & Divisive' remains visible throughout.

3. The two dendrograms—one on the left and one on the right—remain static throughout the segment.

The screen displays the two types of hierarchical clustering: agglomerative and divisive, illustrated using dendrograms to represent the hierarchical structure—from individual points merging into clusters, or from an overall cluster splitting downward. Since this segment contains only closing remarks, it does not include step-by-step explanations of these diagrams.

1. Audio
   Observation

   The instructor uses the counterexample 'सबको 50% off' to illustrate that performing a one-time, undifferentiated grouping is insufficiently fine-grained.

2. Audio
   Observation

   The instructor then emphasizes building clusters first, then building hierarchy—handling different groups separately.

Assuming clustering merely requires dividing similar objects into several groups, without considering further hierarchical relationships among those groups.

The video explicitly states that the key to hierarchical clustering lies in the fact that clusters themselves can form relations, thereby supporting finer segmentation of target audiences.

1. Caption evidence
   Observation

   Only 'Agglomerative & Divisive' is written on the slide.

2. Audio
   Observation

   The instructor identifies these two as types of hierarchical clustering.

1. The video does not state whether these are all possible subtypes or merely the two main ones.

Assuming that the entire subject of hierarchical clustering is limited to just these two terms and requires no further details.

This section introduces only agglomerative and divisive clustering; detailed algorithms, linkage criteria, and further steps are not shown here.

1. Diagram
   Observation

   Only partial entries with 1, 5, and 8 are displayed.

2. Audio
   Observation

   The instructor mentions constructing a proximity matrix.

1. Because the full matrix is not shown, it may be misleading to think this portion alone is sufficient.

Understanding that the small portion shown on the board is the entire proximity matrix.

Only a partial example is shown in the video; the full $6\times 6$ matrix is not presented in this section.

1. Audio
   Observation

   The instructor only discusses merging the pair with the smallest distance.

2. Diagram
   Observation

   Terms such as single-linkage, complete-linkage, and average-linkage are not written.

Assuming that the simple minimum-distance rule shown here constitutes the full linkage method of hierarchical clustering.

This section does not provide the formal name or detailed rule for linkage; only an illustrative merge is shown.

1. Audio
   Observation

   The instructor explicitly contrasts 'going from bottom to up' with 'going from top to down, but here you go from bottom to up'.

It is easy to assume that the two hierarchical clustering methods differ only in name, with no essential difference in their procedural direction.

The video emphasizes that agglomerative clustering proceeds upward from individual points at the bottom, while divisive clustering proceeds downward from the full set at the top—these directions are opposite.

1. Audio
   Observation

   The instructor says, '5 and 8 are combined in this way.'

2. Diagram
   Observation

   The board writing actually shows (5,(8,10)), indicating that 5 is merged with the entire cluster (8,10).

1. This reflects the difference between oral brevity and strict notation on the board—not an explicit correction statement.

Upon hearing 'merge 5 and 8', one might mistakenly assume only two original points are merged each time.

According to the board notes, 5 is actually merged into the already-formed cluster (8,10); hierarchical clustering allows merging a 'point' with a 'cluster'.

1. Audio
   Observation

   The instructor first explains the concept of hierarchical clustering, then says 'दो तरीके से आप लोग create कर सकते हो एक agglomerative और एक divisive'.

2. Diagram
   Observation

   The slide lists 'Agglomerative & Divisive' directly under the 'Hierarchical clustering' heading.

The video presents agglomerative and divisive as two ways to create hierarchical clustering, so they are two branches under the overarching concept.

1. Audio
   Observation

   The instructor first gives intuitive definitions of clustering and hierarchy, then moves to an e-commerce example from a business point of view.

The e-commerce customer segmentation example applies the fundamental idea introduced earlier: 'similar points in the same cluster, and clusters further stratified.'

1. Audio
   Observation

   After explaining the business motivation, the instructor naturally introduces 'two approaches'—namely, agglomerative and divisive.

The video's logic is: because the business requires a more refined hierarchical targeting of audiences, the next step is to introduce the two methodological pathways for implementing hierarchical clustering.

1. Caption evidence
   Observation

   Under 'Hierarchical clustering', 'Agglomerative & Divisive' is written.

Agglomerative clustering is a type of hierarchical clustering, presented in this section as a bottom-up approach.

1. Audio
   Observation

   First, one constructs a proximity matrix; then, one merges the pair with the smallest distance.

Pairwise distances are needed to choose which merge to perform, so the proximity matrix is a prerequisite for the agglomerative merge step.

1. Audio
   Observation

   The instructor explains using a simple example and then demonstrates the merge steps on that same example.

The numerical example illustrates the agglomerative merge rule in practice.

1. Audio
   Observation

   The instructor describes divisive clustering as division-based and top-down.

In this section, divisive clustering is presented as a top-down approach, opposite to agglomerative clustering.

1. Diagram
   Observation

   The whiteboard subtitle lists Agglomerative as a type of Hierarchical clustering.

The agglomerative approach is a specific construction method for hierarchical clustering.

1. Diagram
   Observation

   The whiteboard subtitle also lists Divisive as a type of Hierarchical clustering.

The divisive approach is also a specific construction method for hierarchical clustering.

1. Audio
   Observation

   The instructor explicitly contrasts bottom-up with top-down.

Both are hierarchical clustering methods, but one proceeds upward by merging, while the other proceeds downward by splitting.

1. Audio
   Observation

   The instructor says 'We call this a dendrogram.'

2. Diagram
   Observation

   The label appears directly beside the newly completed hierarchical tree.

A dendrogram is a graphical representation of the result of hierarchical clustering.

1. Audio
   Observation

   The instructor says that Python's scipy library can be used to create this structure.

scipy is mentioned as a tool for implementing or plotting a dendrogram.

1. Audio
   Observation

   At the beginning of this segment, hierarchical clustering's basic meaning is directly stated and explained.

1. Intuitive definition of hierarchical clustering

1. Audio
   Observation

   The instructor uses an e-commerce promotion example to explain why hierarchy is needed.

1. Business motivation for hierarchical clustering
2. E-commerce customer segmentation discount example

1. Audio
   Observation

   At the end of this segment, the instructor explicitly names the two methods: agglomerative and divisive.

2. Diagram
   Observation

   The slide's bullet point also reads 'Agglomerative & Divisive'.

1. This segment only provides the names and an initial hint about agglomerative—it does not fully explain the differences between the two.

1. The two method names of hierarchical clustering.

1. Caption evidence
   Observation

   Both the title and the bullet points show both types.

1. Two types of hierarchical clustering

1. Audio
   Observation

   First, one constructs a proximity matrix.

1. Proximity matrix
2. The merge rule for agglomerative clustering

1. Audio
   Observation

   It is about merging the pair with the smallest distance.

1. An example of agglomerative clustering on one-dimensional numbers.
2. The pair with the minimum distance merges first.

1. Audio
   Observation

   The instructor mentions reducing six items to four.

1. An example of agglomerative clustering on one-dimensional numbers.
2. The merge rule for agglomerative clustering

1. Audio
   Observation

   A comparison between bottom-up and top-down approaches is presented.

1. Two types of hierarchical clustering
2. Agglomerative is bottom-up; divisive is top-down.

1. Diagram
   Observation

   The title 'Hierarchical clustering' runs throughout the segment.

1. Hierarchical clustering

1. Diagram
   Observation

   On the left, merging proceeds step by step into a tree.

1. agglomerative hierarchical clustering
2. Step-by-step construction of an agglomerative tree
3. Hierarchical clustering example with six points

1. Diagram
   Observation

   On the right, splitting proceeds downward from the full set.

1. Divisive hierarchical clustering
2. Step-by-step construction of a divisive tree
3. Hierarchical clustering example with six points

1. Audio
   Observation

   The instructor explicitly contrasts the two directions.

1. agglomerative hierarchical clustering
2. Divisive hierarchical clustering
3. Agglomerative is bottom-up.
4. Divisive is top-down.
5. Do not confuse the directions of agglomerative and divisive methods.