# An application of model-based clustering in market segmentation  (Page 3/5)

 Page 3 / 5
1. Random Component: Distribution of $\left\{{Y}_{t}|{Y}_{t-1},\cdots \right\}$ belongs to the exponential family of distributions.
$f\left({y}_{t};{\theta }_{t},\phi |\mathcal{F}\right)=exp\left\{\frac{{y}_{t}{\theta }_{t}-b\left({\theta }_{t}\right)}{{a}_{t}\left({\theta }_{t}\right)},+,c,\left({y}_{t},\phi \right)\right\},$
where θ t is the parameter of the distribution and φ is a dispersion parameter. In the Poisson case, we have: ${a}_{t}\left(\phi \right)=1$ ; ${\theta }_{t}=log\left({\mu }_{t}\right)$ ; $b\left({\theta }_{t}\right)={\mu }_{t}$ ; $c\left({y}_{t};\phi \right)=-logy\phantom{\rule{-0.166667em}{0ex}}$ .
2. Systematic Component: μ t , the mean of Y t , is modeled by a monotone link function $g\left(·\right)$ such that
$g\left({\mu }_{t}\right)={X}_{t}^{T}\beta ,$
where X is the set of covariates and β is a vector of coefficients. In the Poisson case $\mu =\lambda$ , $g\left(\lambda \right)=log\left(\lambda \right)$ .

In the case of time series data, we can augment the exogenous covariates in the model with lagged values of the response variable, i.e. the observed counts at previous time points. Thus the model is “observation-driven.” Lags of exogenous covariates can also be included. For instance let the new covariate matrix be represented by Z , where

${Z}_{t}^{T}=\left({X}_{t},{X}_{t-1},\cdots ,{X}_{t-p},{Y}_{t-1},\cdots ,{Y}_{t-n}\right).$

For more details see [link] .

## Clustering of tsc models

Armed with the GLM model for Poisson regression, we can begin clustering the TSC. In order to determine the similarity or dissimilarity between two TSC, a metric is needed to measure the “distance.” The classic Euclidean metric is not adequate for data with time dependence. We will use the empirical Kullback-Leibler (KL) likelihood metric [link] , which calculates the distance between two TSC by evaluating the relative fit of their respective models.

Let λ j be a given “model structure” for the data, i.e. an observation-driven Poisson model with specified covariates. The KL metric has the following expression.

${D}^{K}\left({\lambda }_{k},{\lambda }_{j}\right)=\frac{1}{|{Y}_{K}|}\sum _{y\in {Y}_{K}}\left(logp\left(y|{\lambda }_{k}\right)-logp\left(y|{\lambda }_{j}\right)\right)$

where Y K is the set of data objects which belong to cluster k . Note that $logp\left(y|{\lambda }_{k}\right)$ is an expression for the likelihood of the model. See [link] for discussion on the likelihood of observation-driven Poisson models. The measure is made symmetric by,

${D}_{S}^{K}=\frac{{D}^{K}\left({\lambda }_{k},{\lambda }_{j}\right)+{D}^{K}\left({\lambda }_{j},{\lambda }_{k}\right)}{2}$

With the KL metric, we apply a hierarchical bottom-up clustering algorithm. A flowchart of the algorithm is displayed in Figure 1.

The algorithm produces a cluster tree similar to the figure below. The bottom-up clustering method is easy to visualize and break down objects into groups and eliminates the need for any stopping criterion.

## Finding relevant data

Though count data are prevalent in consumer behavior, obtaining commercial commercial data for MBC is expensive. Thus, for this project, we use results from previous studies on marketing data to creat a data set that realistically mimics consumer behavior.

## Data simulation

Niraj et al. [link] proposed an economic model for consumer purchases of bacon and eggs. Based on store scanner data, the authors studied the consumer sensitivities to various variables such as personal utility, product prices, product displays, and purchase history. For the purpose of data simulation, key elements from this economic model were borrowed to create our own consumer bacon and eggs purchase data.

We let ${Y}_{b,t}$ and ${Y}_{e,t}$ be a bivariate Poisson random variable which represent a consumer's purchase of bacon and eggs during time window t respectively, then ${Y}_{b,t}$ and ${Y}_{e,t}$ can be modeled using a trivariate reduction [link] :

#### Questions & Answers

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!