Similarity and Dissimilarity ,Biclustering

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• Measuring (dis)similarity -Evaluating output of
  clustering methods Spectral clustering-
  Hierarchical clustering- Agglomerative
  clustering- Divisive clustering- Choosing the
  number of clusters- Clustering data points and
  features- Bi-clustering- Multi-view clustering
  -K-Means clustering- K-meloids clustering-
  Application image segmentation using K- means
  clustering

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What are similarity and dissimilarity
measures?

• Similarities are usually non-negative and are
  often between 0 (no similarity) and 1(complete
  similarity). The dissimilarity between two
  objects is the numerical measure of the degree to
  which the two objects are different.
  Dissimilarity is lower for more similar pairs of
  objects.

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• Manhattan distance is a metric in which the
  distance between two points is the sum of the
  absolute differences of their Cartesian
  coordinates.
• In simple language, it is the absolute sum of
  the difference between the x-coordinates  and
  y-coordinates of each of the points.
• Suppose we have a point A and a point B.
• To find the Manhattan distance between them, we
  just have to sum up the absolute variation along
  the x and y axes.
• We find Manhattan distance between two points by
  measuring along axis at right angles.In a plane
  with p1 at (x1, y1) and p2 at (x2, y2).Manhattan
  distance x1 x2 y1 y2

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Clustering in Machine Learning

• Clustering or cluster analysis is a machine
  learning technique, which groups the unlabelled
  dataset.
• It can be defined as "A way of grouping the data
  points into different clusters, consisting of
  similar data points.
• The objects with the possible similarities remain
  in a group that has less or no similarities with
  another group."

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• It does it by finding some similar patterns in
  the unlabelled dataset such as shape, size,
  color, behavior, etc., and divides them as per
  the presence and absence of those similar
  patterns.
• It is an unsupervised learning method, hence no
  supervision is provided to the algorithm, and it
  deals with the unlabeled dataset.
• After applying this clustering technique, each
  cluster or group is provided with a cluster-ID.
  ML system can use this id to simplify the
  processing of large and complex datasets.

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• Example Let's understand the clustering
  technique with the real-world example of Mall
  When we visit any shopping mall, we can observe
  that the things with similar usage are grouped
  together. Such as the t-shirts are grouped in one
  section, and trousers are at other sections,
  similarly, at vegetable sections, apples,
  bananas, Mangoes, etc., are grouped in separate
  sections, so that we can easily find out the
  things.
• The clustering technique also works in the same
  way. Other examples of clustering are grouping
  documents according to the topic.
• The clustering technique can be widely used in
  various tasks. Some most common uses of this
  technique are
• Market Segmentation
• Statistical data analysis
• Social network analysis
• Image segmentation
• etc.

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• Apart from these general usages, it is used by
  the Amazon in its recommendation system to
  provide the recommendations as per the past
  search of products. 
• Netflix also uses this technique to recommend the
  movies and web-series to its users as per the
  watch history.
• The below diagram explains the working of the
  clustering algorithm. We can see the different
  fruits are divided into several groups with
  similar properties.

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What is spectral clustering algorithm?

• Spectral clustering is a technique with roots in
  graph theory, where the approach is used to
  identify communities of nodes in a graph based on
  the edges connecting them.
• The method is flexible and allows us to cluster
  non graph data as well.

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To perform a spectral clustering we need 3 main
steps

• Create a similarity graph between our N objects
  to cluster.
• Compute the first k eigenvectors of its Laplacian
  matrix to define a feature vector for each
  object.
• Run k-means on these features to separate objects
  into k classes.

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Spectral Clustering Matrix Representation

• Adjacency and Affinity Matrix (A)

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Degree Matrix (D)

• A Degree Matrix is a diagonal matrix, where the
  degree of a node (i.e. values) of the diagonal is
  given by the number of edges connected to it.
• We can also obtain the degree of the nodes by
  taking the sum of each row in the adjacency
  matrix.

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Laplacian Matrix (L)

• This is another representation of the graph/data
  points, which attributes to the beautiful
  properties leveraged by Spectral Clustering.
• One such representation is obtained by
  subtracting the Adjacency Matrix from the Degree
  Matrix (i.e. L D A).

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Choosing the number of clusters in hierarchical
clustering

• To get the optimal number of clusters for
  hierarchical clustering, we make use a dendrogram
  which is tree-like chart that shows the sequences
  of merges or splits of clusters.
• If two clusters are merged, the dendrogram will
  join them in a graph and the height of the join
  will be the distance between those clusters.

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How do you select the number of clusters in
hierarchical clustering?

• Decide the number of clusters (k) Select k random
  points from the data as centroid. Assign all the
  points to the nearest cluster centroid. Calculate
  the centroid of newly formed clusters.

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How do you determine the number of clusters?

• Compute clustering algorithm (e.g., k-means
  clustering) for different values of k. ...
• For each k, calculate the total within-cluster
  sum of square (wss).
• Plot the curve of wss according to the number of
  clusters k.

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Do we need to define the number of clusters in
advance for hierarchical clustering?

• Hierarchical clustering does not require you to
  pre-specify the number of clusters, the way that
  k-means does, but you do select a number of
  clusters from your output.

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Clustering data points and features

• Clustering is the task of dividing the population
  or data points into a number of groups such that
  data points in the same groups are more similar
  to other data points in the same group than those
  in other groups. In simple words, the aim is to
  segregate groups with similar traits and assign
  them into clusters.

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What are features in clustering?

• A clustering feature is essentially a summary of
  the statistics for the given cluster.
• Using a clustering feature, we can easily derive
  many useful statistics of a cluster. For example,
  the cluster's centroid, x0, radius, R, and
  diameter, D, are.

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What is clustering in business intelligence?

• Cluster analysis or simply clustering is the
  process of partitioning a set of data objects (or
  observations) into subsets. ... In business
  intelligence, clustering can be used to organize
  a large number of customers into groups, where
  customers within a group share strong similar
  characteristics.

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What is Biclustering used for?

• Biclustering is a powerful data mining technique
  that allows clustering of rows and columns,
  simultaneously, in a matrix-format data set. It
  was first applied to gene expression data in
  2000, aiming to identify co-expressed genes under
  a subset of all the conditions/samples.

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What is clustering algorithm in BI?

• The K- Means Clustering algorithm is a process by
  which objects are classified into number of
  groups so that they are as much dissimilar as
  possible from one group to another, and as much
  similar as possible within each group. KMeans
  Clustering is a grouping of similar things or
  data.

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What is multi-view clustering?

• Multi-view graph clustering This category
  of methods seeks to find a fusion graph (or
  network) across all views and then uses graph-cut
  algorithms or other technologies (e.g., spectral
  clustering) on the fusion graph in order to
  produce the clustering result.

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K-mean clustering

• Steps
• Take mean value
• Find the nearest number to mean put it in the
  cluster
• Repeat step 12 until we get same mean .