A partition is an assignment of every element of a set into 1 & only 1 subset w/ no empty subsets. A common instance of partitioning in statistics is the partitioning of sums of squares for F-tests.

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How to build a decision tree with a constraint on sensitivity?

I am trying to develop a classification model on a sample of people which will discriminate between "Type A" and "Not-Type A" people. Due to external factors, the minimum sensitivity for this ...
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5 views

How to compare multiple non-hierarchical classications of the same dataset

I'm a taxonomist working on an identification consistency project in which a couple dozen researchers were asked to manually classify the same set of images into like groups. Each classification will ...
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1answer
41 views

Least Squared Regressions on Partitioned Data

Say I have 800 (X,Y) data points, and I do a LSQ fit and get y = mx+b Then I think to myself, of the 800 data points, 500 are males and 300 are females, so I ...
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64 views

What are the differences between Lloyd's, MacQueen's and Hartigan's algorithms for K-Means?

There are three distinct algorithms for the K-Means function in R. These are: Lloyd's MacQueen's Hartigan's I believe I understand how Lloyd's works. 1. The cluster centers are chosen. 2. Points ...
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119 views

Multiple eigenvectors in graph spectral clustering

In Newman's PNAS 2006 paper Modularity and community structure in networks, the first eigenvector splits the graph in two clusters, and then each cluster can be further divided by eigenvector of a ...
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6 views

Comparing groups that themselves are calculated from means

Context: I am calculating net energy benefit from a series of energy costs and gross energy benefits. For example, I have 3 measurements of gross benefit, replicated 4 times, for each of 4 ...
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26 views

Is K-Medoids really better at dealing with outliers than K-Means? (with example showing the contrary)

K-Medoids and K-Means are two popular methods of partitional clustering. The consensus is that K-Medoids is better at clustering data when there are outliers (source). This is because it chooses data ...
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7 views

Efficient ways to partition rows of augmented design matrix $[X|y]$ into subsets with similar regression results?

Imagine I have $n$ observations on a regression model; are there any reasonably efficient methods for partitioning that into two (or more) roughly equally sized groups which almost reproduce the ...
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81 views

Catalan numbers and gambler's ruin paths

In a lecture on catalan numbers for an analysis of algorithms course hosted on coursera (https://www.coursera.org/course/aofa), the professor states that the number of gambler's ruin paths containing ...
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30 views

Comparing two graphs/markov chains by comparing their clusters

I have an undirected graph representation of my system (a dynamical system), i.e. I have some labelled nodes and bi-directional edge weights, so everything is in a Markov matrix form. Now I can form ...
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15 views

Structural partition for cross validation

Can the partitioning of data for cross validation be used structurally to assess the transfer ability of an effect of one factor across another factor? A MANOVA performed on multivariate data reveals ...
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1answer
19 views

Clustering a list of restaurant dishes

If I have a large list of restaurant dishes that all have the same cuisine... (Pulled Pork, BBQ chicken, 1/2 Ribs, Pork Sliders, Slow Smoked Pork, Full Chicken Special....) What would be a good ...
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1answer
48 views

Partition data into two sets such that the difference of their variance is minimal

Suppose there are $n$ data values $x_1<x_2<\ldots<x_{n-1}<x_n$,and I've found a partition number $k$, such that $$ ...
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45 views

How to partition $R^2$ among predictors in multiple regression with interaction terms in R

Say I have some predictors, and I know how they affect some dependent variable: ...
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0answers
23 views

How does the polr command in R handle partitioning variance?

I am using ordinal regression (MASS package, polr command) to analyze ranked coloration data (% piebaldism) of an iguana species based on sex, snout-vent length (SVL), and location. I'm concerned that ...
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37 views

mean square distortion of quantization data set

I am using the matlab function lloyds to cluster a 1-dimensional timeseries. [partition,codebook,distor] = lloyds(training_set,initcodebook); and I get that the ...
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2answers
118 views

Representative elements of a set

I'm looking for the technical name of the following problem. It sounds like a standard machine learning technique, but I'm not familiar with the field, and can't seem to find it. Let's say that we ...
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1answer
58 views

Visualise variance partitioning

I'm interested in visualising variance partitioning in the context of linear models. Say you run an linear regression that predicts peoples weight based on their height and age. How can you visualise ...
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1answer
91 views

K-Medoids swapping inside clusters

I'm a bit confused with concept of K-medoids. It seems that original algorithm (PAM) describes that swap step should be performed by swaping only one of the medoids with one non-medoid point from ...
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2answers
278 views

Data partitioning according two variables

I am working with the following dataset: ...
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1answer
82 views

Show that $\sqrt{ESS} \leq \sqrt{ESS_{A}}+\sqrt{ESS_{\bar{A}}}$ where ESS=Explained sum of squares

Suppose we have a dependent variable $Y$ with mean zero and set of regressors which we divide into two sets, $A$ and $\bar{A}$. Let $ESS$ denote the explained sum of squares (ESS) from regressing $Y$ ...
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60 views

Creating two clusters with as equal centroids as possible

I have a number of data points that can be placed in a 2D-space according to two variables, in this case named "Variable_1" and "Variable_2", like so: ...
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1answer
132 views

Clustering into teams of fixed size

There is a particular team-based video game that exposes a ladder of individual ratings for each player that looks like this (player, rating, wins, losses): A, 2000, 35, 12 B, 1900, 41, 19 C, 1800, ...
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22 views

Partitioning Spatial Dependence?

So, I have a group of nations that exhibit global spatial dependence. I want to partition the nations into groups so that, at an intuitive level at least, the "sum of the spatial dependence within ...
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4answers
1k views

How to split dataset for time-series prediction?

I have historic sales data from a bakery (daily, over 3 years). Now I want to build a model to predict future sales (using features like weekday, weather variables, etc.). How should I split the ...
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1answer
63 views

What is an equi-depth partition of the data?

In the paper Outlier Detection for High Dimensional Data at the beginning of section 1.3 Is written: Each attribute of the data is divided into $\phi$ equi-depth ranges. Thus, each range contains ...
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2answers
87 views

How can I partition a distribution into two sub-populations with fixed bias? (simulation)

I am trying to simulate a selection model for a variable $Y$ dependent on covariate vector $X$, so that two groups/sub-sets $S=(0,1)$ of observations on $Y$ are created, which have a fixed difference ...
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2answers
105 views

Assigning even partitions for Cross-Validation

This is a very basic question about cross-validation. Say that I have a sample size of 2901(or any difficult to divide number). How do I split this up into equal partitions (other than n=1)? And how ...
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1answer
83 views

Need help understanding response from Metis

I was wondering if any of you could help me understand the response I got from this clustering algorithm (Metis). As you probably can see, I'm trying to cluster IP addresses based on common records ...
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1answer
168 views

How do multi-attribute edge-weights influence community detection?

My graph consists of a computer network topology where each vertex is a physical node/device (depicted using its IP address). Two vertices will have an edge if the nodes have had communication with ...
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1k views

Using a Decision Tree Algorithm such as C4.5 to understand population Partition

I have multivariate data about a certain population with more than 1000 attributes per exemplar. Some of the variables are basic demographics attributes including: gender, age, race, ethnicity, ...
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1answer
469 views

Nested ANOVA: Unequal sample sizes? Variance components?

I am completely out of my depth on this, and all the reading I try to do just confuses me. I'm hoping you can explain things to me in a way that makes sense. (As always seems to be the case, "It ...
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186 views

Partitioning variance from logistic regression

Short version How can I partition the variance from the different levels in a nested mixed-effects logistic regression? Preferably using R, but even general principles would be helpful as a start. ...
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886 views

is it possible to use partitioned data(train&test) together with cross-fold validation?

I have used SPSS Clementine in order to train a classifier, for this I have used a partition node with 2 parts(train and test),then using a c5-tree and cross-fold validation. I did this because I ...
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901 views

R procedure for comparing multiple categorical variables (similar to anova() followed by t.test() for continuous)?

Big Picture: How can I implement partitioned Chi Square in R? I understand how to perform the overall Chi square, and then how to get individual parameters (observed counts, expected counts, ...
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1k views

Does Newman's network modularity work for signed, weighted graphs?

The modularity of a graph is defined on its Wikipedia page. In a different post, somebody explained that modularity can easily be computed (and maximized) for weighted networks because the adjacency ...
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2answers
339 views

Class labels in data partitions

Suppose that one partitions the data to training/validation/test sets for further application of some classification algorithm, and it happens that training set doesn't contain all class labels that ...
2
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1answer
210 views

How interactions between explanatory variables can be found using binary recursive partitioning?

I would like to investigate interactions between my explanatory variables prior to building a statsitical model. Apparently it is possible to do it in R using a regression tree (library: tree). This ...
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268 views

Modularity of graph: why are probabilities of self-loop included?

I'm trying to understand the Newman Modularity (doi:10.1073/pnas.0601602103) by investigating its calculation on the Wikipedia example . My question is why are probabilities of self-loops included in ...
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1answer
2k views

Correct way of evaluating Random Forest performance wrt training/test, feature selection, ntrees, random seed

I need to use Random Forest in my experiments. Although using the same training and test datasets, each time that I train the Random Forest on my training set, I get a different result on my test set. ...
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138 views

Variance partitioning - why be cautious?

I'm about to use variance partitioning to interpret my results of a given model and across models and have come across various criticisms of it most notably by Pedhazur (1982, 1997). Also, the ...
2
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1answer
815 views

Partitioning Around Medoids

I have a question regarding Partitioning Around Medoids (PAM) clustering algorithm, because everywhere I look, it is described differently. In every step of the algorithms do I swap only one medoid or ...
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31 views

Testing that a finite quantity is equally partitioned

Suppose I have a set of observations on a finite (continuously divisible) quantity $Q$ (say $Q = 100$ to be concrete). For each observation $i$, $Q$ is partitioned into three parts $(A_i, B_i, C_i)$, ...
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103 views

Discretization of skewed data (time durations)

I have data that describes the duration of how long a person views a webpage. This is quite varied and in the context wherein I gathered the data, it was very skewed. People mostly spent short amounts ...
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1answer
245 views

Multivariate Gaussian with 3 Partitions

Given that we partition a Gaussian random vector $\textbf{x}$ into three groups, $\textbf{x}_a$, $\textbf{x}_b$, and $\textbf{x}_c$, with a corresponding partitioning of the mean vector $\mu$ and of ...
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2answers
197 views

Linear SVM C optimisation data, how to partition into train, model construction, test

My aim is to find the best C for a linear SVM classification using libsvm, I have 120 instances in total and 2 classes which I want to classify. I have question regarding partitioning a the dataset ...
5
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1answer
796 views

Is $R^2$ value valid for insignificant OLS regression model?

I am interested in stating that ___ % of the variance in Y is explained uniquely by $X_1$ and ___ % is explained uniquely by $X_2$. Is there some way to obtain this from a multiple regression ...
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157 views

How to Partition An Interaction SS in ANOVA

I'm a new user of R and I'm trying to replicate Table 6.18 on page 262 in Statistical Procedures in Agricultural Research, By K. A. Gomez and A. A. Gomez. New York, Chichester, etc.: Wiley (1984). ...
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1answer
279 views

Can I partition a frequency table and use Fisher's exact test instead of the chi-squared test?

I am working with very small cell counts, and am wondering if Fisher's exact test can be used in place of the chi-squared test when partitioning IxJ tables. I am interested if the same process for ...
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1answer
509 views

mobForest R Package

I have recently begún to learn about model based recursive partitioning by playing around with MOB in the party package. I came across this mobForest package but am a little baffled towards what it is ...