Question

Sometimes a set of data has a very large range (very small numbers to very big num- bers). This is often the case with signal-to-noise ratios in electronics, or turbulent kinetic energy in fluid mechanics. In this case it may make sense to plot one or both of the axes on a log scale Rather than use a SNR or TKE data set (which take some engineering content back- ground to understand), we're going to explore semilog and log-log plots using the function KE = 1000k-5/3 (The 1000 is arbitrary, but the -5/3 is a very special value in turbulent fluid mechan- 1CS First, look at the help information on the Matlab functions semilogx, semilogy and loglog. (They work very much like the plot command.) Next, plot TKE k rela- tionship for values of k from 10 to 10,000, using the plot, semilogx, semilogy and loglog commands. Put them in a single figure using the subplot command. Be sure to properly label and title the plots. Your resulting figure should look like this: normal plot semilogx plot 20 20 10 10 10000 10 10 10 semilogy plot log-log plot 10 10 10 10 5000 10000 10 4 10

plot relationship using the plot, semilogx, semilogy, and loglog commands.

I cannot understand how to use the semilogx, semilogy, and loglog commands, and my graphs are completely wrong when conmpared to the answer

Answer 1

The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms.^[4] There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:

• Connectivity models: for example, hierarchical clustering builds models based on distance connectivity.
• Centroid models: for example, the k-means algorithm represents each cluster by a single mean vector.
• Distribution models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the Expectation-maximization algorithm.
• Density models: for example, DBSCAN and OPTICS defines clusters as connected dense regions in the data space.
• Subspace models: in Biclustering (also known as Co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes.
• Group models: some algorithms do not provide a refined model for their results and just provide the grouping information.
• Graph-based models: a clique, that is, a subset of nodes in a graph such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster. Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques, as in the HCS clustering algorithm.

A "clustering" is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. Clusterings can be roughly distinguished as:

• hard clustering: each object belongs to a cluster or not
• soft clustering (also: fuzzy clustering): each object belongs to each cluster to a certain degree (for example, a likelihood of belonging to the cluster)

There are also finer distinctions possible, for example:

• strict partitioning clustering: here each object belongs to exactly one cluster
• strict partitioning clustering with outliers: objects can also belong to no cluster, and are considered outliers.
• overlapping clustering (also: alternative clustering, multi-view clustering): while usually a hard clustering, objects may belong to more than one cluster.
• hierarchical clustering: objects that belong to a child cluster also belong to the parent cluster
• subspace clustering: while an overlapping clustering, within a uniquely defined subspace, clusters are not expected to overlap.