Hierarchical clustering is a widely used method in data analysis and data mining that aims to group similar data points into clusters based on their characteristics or attributes. This clustering technique organizes the data into a hierarchical structure, creating a nested series of clusters where each cluster contains subclusters of increasingly similar data points.
The primary purpose of hierarchical clustering is to uncover underlying patterns or structures in a dataset by grouping similar data points together. By organizing the data into a hierarchical structure of clusters, this clustering technique enables analysts to explore the relationships and similarities between different data points and identify meaningful groupings or clusters that can inform decision-making and analysis.
Process of Hierarchical Clustering
The process of hierarchical clustering typically involves the following steps:
1. Distance Computation
Begin by calculating the pairwise distances or similarities between all pairs of data points in the dataset. The choice of distance metric depends on the nature of the data and the problem domain but commonly used metrics include Euclidean distance, Manhattan distance, and cosine similarity.
2. Cluster Initialization
Initialize each data point as a separate cluster or assign each data point to its own cluster.
3. Cluster Merging
Iteratively merge the most similar clusters based on their distance or similarity until all data points are grouped into a single cluster. The choice of merging criterion depends on the specific algorithm used for hierarchical clustering and can include methods such as single linkage, complete linkage, average linkage, and Ward’s method.
4. Dendrogram Construction
Construct a dendrogram, which is a tree-like diagram that represents the hierarchical structure of the clusters. The dendrogram visually depicts the sequence of cluster mergings and allows analysts to visualize the relationships between clusters and subclusters.
5. Cluster Selection
Determine the optimal number of clusters by inspecting the dendrogram or using methods such as the elbow method or silhouette analysis. The goal is to identify a level of clustering that maximizes the cohesion within clusters while minimizing the separation between clusters.
Types of Hierarchical Clustering
There are two main types of hierarchical clustering:
1. Agglomerative Hierarchical Clustering
In agglomerative hierarchical clustering, also known as bottom-up clustering, each data point initially forms its own cluster, and pairs of clusters are iteratively merged based on their similarity until all data points belong to a single cluster.
2. Divisive Hierarchical Clustering
In divisive hierarchical clustering, also known as top-down clustering, all data points initially belong to a single cluster, and the clustering process involves recursively dividing the data into smaller clusters based on their dissimilarity until each data point is in its own cluster.
Applications of Hierarchical Clustering
Hierarchical clustering has numerous applications across various domains, including:
Biology and Bioinformatics: Hierarchical clustering is used to analyze gene expression data, DNA sequencing data, and protein-protein interaction networks to identify clusters of genes or proteins with similar functions or regulatory patterns.
Market Segmentation: Hierarchical clustering is used in marketing and market research to segment customers or products into distinct groups based on their characteristics or purchasing behavior.
Image Segmentation: Hierarchical clustering is used in computer vision and image processing to segment images into regions or objects with similar visual features, such as color, texture, or shape.
Text Mining: Hierarchical clustering is used in natural language processing and text mining to cluster documents, articles, or text snippets based on their semantic similarity or topic.
Anomaly Detection: Hierarchical clustering is used in anomaly detection and fraud detection to identify unusual patterns or outliers in large datasets by clustering normal data points and flagging data points that do not belong to any cluster.
Best Practices for Hierarchical Clustering
To ensure the effectiveness and reliability of hierarchical clustering analyses, consider the following best practices:
1. Data Preprocessing
Preprocess the data to remove noise, handle missing values, and standardize or normalize the features to ensure that all variables contribute equally to the clustering process.
2. Distance Metric Selection
Choose an appropriate distance metric or similarity measure that is suitable for the data and the problem domain. Experiment with different distance metrics to find the one that best captures the underlying relationships between data points.
3. Linkage Criterion Selection
Select an appropriate linkage criterion or merging criterion that defines how the similarity between clusters is computed during the clustering process. Evaluate different linkage criteria to determine which one produces the most meaningful and interpretable clusters.
4. Dendrogram Interpretation
Carefully interpret the dendrogram to identify the optimal number of clusters and determine the hierarchical structure of the clusters. Consider factors such as cluster cohesion, cluster separation, and the stability of the clustering solution.
5. Validation and Evaluation
Validate and evaluate the clustering results using internal validation metrics, such as silhouette score or Davies-Bouldin index, and external validation measures, such as cluster purity or Rand index. Compare different clustering solutions and select the one that best meets the objectives of the analysis.
Conclusion
Hierarchical clustering is a versatile and powerful technique for uncovering patterns and structures in data by grouping similar data points into clusters.
By organizing the data into a hierarchical structure of clusters, hierarchical clustering enables analysts to explore the relationships between data points and identify meaningful groupings that can inform decision-making and analysis across various domains.
By following best practices and considering factors such as data preprocessing, distance metric selection, and dendrogram interpretation, analysts can ensure the effectiveness and reliability of hierarchical clustering analyses and derive actionable insights from their data.
Whether used in biology, marketing, image processing, or anomaly detection, hierarchical clustering offers a valuable approach for exploring and understanding complex datasets and unlocking hidden patterns and relationships within them.
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
Occam’s Razor states that one should not increase (beyond reason) the number of entities required to explain anything. All things being equal, the simplest solution is often the best one. The principle is attributed to 14th-century English theologian William of Ockham.
The Lindy Effect is a theory about the ageing of non-perishable things, like technology or ideas. Popularized by author Nicholas Nassim Taleb, the Lindy Effect states that non-perishable things like technology age – linearly – in reverse. Therefore, the older an idea or a technology, the same will be its life expectancy.
Antifragility was first coined as a term by author, and options trader Nassim Nicholas Taleb. Antifragility is a characteristic of systems that thrive as a result of stressors, volatility, and randomness. Therefore, Antifragile is the opposite of fragile. Where a fragile thing breaks up to volatility; a robust thing resists volatility. An antifragile thing gets stronger from volatility (provided the level of stressors and randomness doesn’t pass a certain threshold).
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.
Maslow’s Hammer, otherwise known as the law of the instrument or the Einstellung effect, is a cognitive bias causing an over-reliance on a familiar tool. This can be expressed as the tendency to overuse a known tool (perhaps a hammer) to solve issues that might require a different tool. This problem is persistent in the business world where perhaps known tools or frameworks might be used in the wrong context (like business plans used as planning tools instead of only investors’ pitches).
The Peter Principle was first described by Canadian sociologist Lawrence J. Peter in his 1969 book The Peter Principle. The Peter Principle states that people are continually promoted within an organization until they reach their level of incompetence.
The straw man fallacy describes an argument that misrepresents an opponent’s stance to make rebuttal more convenient. The straw man fallacy is a type of informal logical fallacy, defined as a flaw in the structure of an argument that renders it invalid.
The Streisand Effect is a paradoxical phenomenon where the act of suppressing information to reduce visibility causes it to become more visible. In 2003, Streisand attempted to suppress aerial photographs of her Californian home by suing photographer Kenneth Adelman for an invasion of privacy. Adelman, who Streisand assumed was paparazzi, was instead taking photographs to document and study coastal erosion. In her quest for more privacy, Streisand’s efforts had the opposite effect.
As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.
Goodhart’s Law is named after British monetary policy theorist and economist Charles Goodhart. Speaking at a conference in Sydney in 1975, Goodhart said that “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.” Goodhart’s Law states that when a measure becomes a target, it ceases to be a good measure.
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.
Moore’s law states that the number of transistors on a microchip doubles approximately every two years. This observation was made by Intel co-founder Gordon Moore in 1965 and it become a guiding principle for the semiconductor industry and has had far-reaching implications for technology as a whole.
Disruptive innovation as a term was first described by Clayton M. Christensen, an American academic and business consultant whom The Economist called “the most influential management thinker of his time.” Disruptive innovation describes the process by which a product or service takes hold at the bottom of a market and eventually displaces established competitors, products, firms, or alliances.
Value migration was first described by author Adrian Slywotzky in his 1996 book Value Migration – How to Think Several Moves Ahead of the Competition. Value migration is the transferal of value-creating forces from outdated business models to something better able to satisfy consumer demands.
The bye-now effect describes the tendency for consumers to think of the word “buy” when they read the word “bye”. In a study that tracked diners at a name-your-own-price restaurant, each diner was asked to read one of two phrases before ordering their meal. The first phrase, “so long”, resulted in diners paying an average of $32 per meal. But when diners recited the phrase “bye bye” before ordering, the average price per meal rose to $45.
Groupthink occurs when well-intentioned individuals make non-optimal or irrational decisions based on a belief that dissent is impossible or on a motivation to conform. Groupthink occurs when members of a group reach a consensus without critical reasoning or evaluation of the alternatives and their consequences.
A stereotype is a fixed and over-generalized belief about a particular group or class of people. These beliefs are based on the false assumption that certain characteristics are common to every individual residing in that group. Many stereotypes have a long and sometimes controversial history and are a direct consequence of various political, social, or economic events. Stereotyping is the process of making assumptions about a person or group of people based on various attributes, including gender, race, religion, or physical traits.
Murphy’s Law states that if anything can go wrong, it will go wrong. Murphy’s Law was named after aerospace engineer Edward A. Murphy. During his time working at Edwards Air Force Base in 1949, Murphy cursed a technician who had improperly wired an electrical component and said, “If there is any way to do it wrong, he’ll find it.”
The law of unintended consequences was first mentioned by British philosopher John Locke when writing to parliament about the unintended effects of interest rate rises. However, it was popularized in 1936 by American sociologist Robert K. Merton who looked at unexpected, unanticipated, and unintended consequences and their impact on society.
Fundamental attribution error is a bias people display when judging the behavior of others. The tendency is to over-emphasize personal characteristics and under-emphasize environmental and situational factors.
Outcome bias describes a tendency to evaluate a decision based on its outcome and not on the process by which the decision was reached. In other words, the quality of a decision is only determined once the outcome is known. Outcome bias occurs when a decision is based on the outcome of previous events without regard for how those events developed.
Hindsight bias is the tendency for people to perceive past events as more predictable than they actually were. The result of a presidential election, for example, seems more obvious when the winner is announced. The same can also be said for the avid sports fan who predicted the correct outcome of a match regardless of whether their team won or lost. Hindsight bias, therefore, is the tendency for an individual to convince themselves that they accurately predicted an event before it happened.
Gennaro is the creator of FourWeekMBA, which reached about four million business people, comprising C-level executives, investors, analysts, product managers, and aspiring digital entrepreneurs in 2022 alone | He is also Director of Sales for a high-tech scaleup in the AI Industry | In 2012, Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
