A feature that has different meanings in different ranges - machine-learning

In machine learning, how to deal with a feature like salary. For example, if I'm applying k-nearest neighbors by measuring the distance between data points based on features. Let's say we have two points with salaries 2000 and 6000. The difference between them is 4000. Let's view another two points with salaries 102000 and 106000. The difference here is still 4000$ but we humans consider the last two points closer or more similar than the first two points.
How do I incorporate such an intuition in machine learning?

You can do one of the following things (and many more):
transform the feature using log function (thus 2000 and 6000 would be much further than 102000 and 106000)
binarize feature into multiple buckets (you would create a feature for each range of salary and you are the one creating the buckets)
change similarity function in k-nn to look at relative instead of absolute difference

Related

Hierarchical Clustering

I have read some resources and I found out how hierarchical clustering works. However, when I compare it with k-means clustering, it seems to me that k-means really constitues specific number of clusters,whereas hierarchical analysis shows me how the samples can be clustered. What I mean is that I do not get a specific number of clusters in hierarchical clustering. I get only a scheme about how the clusters can be constituted and portion of relation between the samples.
Thus, I cannot understand where I can use this clustering method.
Hierarchical clustering (HC) is just another distance-based clustering method like k-means. The number of clusters can be roughly determined by cutting the dendrogram represented by HC. Determining the number of clusters in a data set is not an easy task for all clustering methods, which is usually based on your applications. Tuning the thresholds in HC may be more explicit and straightforward for researchers, especially for a very large data set. I think this question is also related.
In k-means clustering k is a hyperparameter that you need to find in order to divide your data points into clusters whereas in hierarchical clustering (lets take one type of hierarchical clustering i.e. agglomerative) firstly you consider all the points in your dataset as a cluster and then merge two clusters based on a similarity metric and repeat this until you get a single cluster. I will explain this with an example.
Suppose initially you have 13 points (x_1,x_2,....,x_13) in your dataset so at start you will have 13 clusters, now in second step lets you get 7 clusters (x_1-x_2 , x_4-x_5, x_6-x_8, x_3-x_7, x_11-x_12, x_10, x_13) based on the similarity between the points. In the third step lets say you get 4 clusters(x_1-x_2-x_4-x_5, x_6-x_8-x_10, x_3-x_7-x_13, x_11-x_12) like this you would arrive to a step wherein all the points in your dataset form one cluster and which is also the last step of agglomerative clustering algorithm.
So in hierarchical clustering, there is no hyperparameter, depending upon your problem, if you want 7 clusters then stop at the second step if you want 4 clusters then stop at the third step and likewise.
A practical advantage in hierarchical clustering is the possibility of visualizing results using dendrogram. If you don’t know in advance what number of clusters you’re looking for (as is often the case…), you can use the dendrogram plot that can help you choose k with no need to create separate clusterings. Dendrogram can also give a great insight into the data structure, help identify outliers, etc. Hierarchical clustering is also deterministic, whereas k-means with random initialization can give you different results when running several times on the same data.
Hope this helps.

Handling geospatial coordinates in machine learning

I'm building a machine learning model where some columns are physical addresses (which I can translate into X / Y coordinates) but I'm a little bit confused on how this will be handled by the ML algorithm.
Is there a particular way to translate a GEO location into columns for use into ML (classification and/or regression) ?
Thanks in advance !
The choice of features would, in general, depend on what kind of relationship you anticipate between the features and the target variable. You are right in saying that post code number itself does not bear any relation to the target. Here the postcode is simply a string, or a category. What kind of model are you planning to use? Linear regression and Decision tree are two examples. These models capture relationships in different ways. As an example for a feature, you could compute the straight line distance between the source and destination, and use that in the model, since intuitively, the farther they are, the higher the transit time is likely to be. What else does the transit time depend on? See if you can relate the factors influencing the travel time to the information that you have, i.e., the postcodes / XY co-ordinates, in some way.
This summarizes the answer we ended up with in the comments of the questions:
This transformation from ZIP codes to geo-coordinates should not be seen as a "split" but only as a way to represent your data in a multidimensional way (in this case the dimension will be 2).
Machine learning algorithms exist for both unidimensional and multidimensional data. The two dimensions can be correlated or uncorrelated, depending on how you define the parameters of the model you choose afterwards.
Moreover, the correlation does not have to be explicitly set in most cases. Only an initial value may be useful, but many algorithm also rely on random initialization or other simple methods that estimate it from a subset of your data. So, for clarity's sake, if you model you data by a Gaussian for example, when estimating the parameters of this Gaussian, the covariance matrix will have non-diagonal term that are non-zeros which will represent the data correlation. You only need not to take an assumption that states that the 2 dimensions are uncorrelated!

DBSCAN using spatial and temporal data

I am looking at data points that have lat, lng, and date/time of event. One of the algorithms I came across when looking at clustering algorithms was DBSCAN. While it works ok at clustering lat and lng, my concern is it will fall apart when incorporating temporal information, since it's not of the same scale or same type of distance.
What are my options for incorporating temporal data into the DBSCAN algorithm?
Look up Generalized DBSCAN by the same authors.
Sander, Jörg; Ester, Martin; Kriegel, Hans-Peter; Xu, Xiaowei (1998). Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications. Data Mining and Knowledge Discovery (Berlin: Springer-Verlag) 2(2): 169–194. doi:10.1023/A:1009745219419.
For (Generalized) DBSCAN, you need two functions:
findNeighbors - get all "related" objects from your database
corePoint - decide whether this set is enough to start a cluster
then you can repeatedly find neighbors to grow the clusters.
Function 1 is where you want to hook into, for example by using two thresholds: one that is geographic and one that is temporal (i.e. within 100 miles, and within 1 hour).
tl;dr you are going to have to modify your feature set, i.e. scaling your date/time to match the magnitude of your geo data.
DBSCAN's input is simply a vector, and the algorithm itself doesn't know that one dimension (time) is orders of magnitudes bigger or smaller than another (distance). Thus, when calculating the density of data points, the difference in scaling will screw it up.
Now I suppose you can modify the algorithm itself to treat different dimensions differently. This can be done by changing the definition of "distance" between two points, i.e. supplying your own distance function, instead of using the default Euclidean distance.
IMHO, though, the easier thing to do is to scale one of your dimension to match another. just multiply your time values by a fixed, linear factor so they are on the same order of magnitude as the geo values, and you should be good to go.
more generally, this is part of the features selection process, which is arguably the most important part of solving any machine learning algorithm. choose the right features, and transform them correctly, and you'd be more than halfway to a solution.

Cluster data with output centers of Kmeans function

Hi I have clustered some data with kmeans function and stored the centers of clusters that it produces as output. Now I have a new set of vectors in a Mat object and want to know to which cluster each vector belongs in. Is there a simple way to do that or should I just calculate the euclidean distances of each vector with all the centers and choose the cluster it is closest to.
If I should go for the second way, are there any efficiency considerations to make it fast?
It seems that you're interested in performing some type of cluster assignment using the results of running K-Means on an initial data set, right?
You could just assign the new observation to the closest mean. Unfortunately with K-Means you don't know anything about the shapes or size of each cluster. For example, consider a scenario where a new vector is equidistant (or roughly equidistant) from two means. What do yo do in this scenario? Do you make a hard assignment to one of the clusters?
In this situation its probably better to actually look at the original data that comprises each of the clusters, and do some type of K-Nearest Neighbor assignment (http://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm). For example, it may turn out that while the new vector is roughly equidistant from two different cluster centers, it is much closer to the data from one of the clusters (indicating that it likely belongs to that cluster).
As an alternative to K-Means, if you used some like Mixture of Gaussians with EM, you'd not only have a set of cluster centers (as you do with K-Means), but also a variance, describing size of the cluster. For each new observation, you could then compute the probability that it belongs to each cluster without revisiting the data from each cluster (as it's baked in to the MoG EM model).

What does dimensionality reduction mean?

What does dimensionality reduction mean exactly?
I searched for its meaning, I just found that it means the transformation of raw data into a more useful form. So what is the benefit of having data in useful form, I mean how can I use it in a practical life (application)?
Dimensionality Reduction is about converting data of very high dimensionality into data of much lower dimensionality such that each of the lower dimensions convey much more information.
This is typically done while solving machine learning problems to get better features for a classification or regression task.
Heres a contrived example - Suppose you have a list of 100 movies and 1000 people and for each person, you know whether they like or dislike each of the 100 movies. So for each instance (which in this case means each person) you have a binary vector of length 100 [position i is 0 if that person dislikes the i'th movie, 1 otherwise ].
You can perform your machine learning task on these vectors directly.. but instead you could decide upon 5 genres of movies and using the data you already have, figure out whether the person likes or dislikes the entire genre and, in this way reduce your data from a vector of size 100 into a vector of size 5 [position i is 1 if the person likes genre i]
The vector of length 5 can be thought of as a good representative of the vector of length 100 because most people might be liking movies only in their preferred genres.
However its not going to be an exact representative because there might be cases where a person hates all movies of a genre except one.
The point is, that the reduced vector conveys most of the information in the larger one while consuming a lot less space and being faster to compute with.
You're question is a little vague, but there's an interesting statistical technique that may be what you're thinking off called Principal Component Analysis which does something similar (and incidentally plotting the results from which was my first real world programming task)
It's a neat, but clever technique which is remarkably widely applicable. I applied it to similarities between protein amino acid sequences, but I've seen it used for analysis everything from relationships between bacteria to malt whisky.
Consider a graph of some attributes of a collection of things where one has two independent variables - to analyse the relationship on these one obviously plots on two dimensions and you might see a scatter of points. if you've three variable you can use a 3D graph, but after that one starts to run out of dimensions.
In PCA one might have dozens or even a hundred or more independent factors, all of which need to be plotted on perpendicular axis. Using PCA one does this, then analyses the resultant multidimensional graph to find the set of two or three axis within the graph which contain the largest amount of information. For example the first Principal Coordinate will be a composite axis (i.e. at some angle through n-dimensional space) which has the most information when the points are plotted along it. The second axis is perpendicular to this (remember this is n-dimensional space, so there's a lot of perpendiculars) which contains the second largest amount of information etc.
Plotting the resultant graph in 2D or 3D will typically give you a visualization of the data which contains a significant amount of the information in the original dataset. It's usual for the technique to be considered valid to be looking for a representation that contains around 70% of the original data - enough to visualize relationships with some confidence that would otherwise not be apparent in the raw statistics. Notice that the technique requires that all factors have the same weight, but given that it's an extremely widely applicable method that deserves to be more widely know and is available in most statistical packages (I did my work on an ICL 2700 in 1980 - which is about as powerful as an iPhone)
http://en.wikipedia.org/wiki/Dimension_reduction
maybe you have heard of PCA (principle component analysis), which is a Dimension reduction algorithm.
Others include LDA, matrix factorization based methods, etc.
Here's a simple example. You have a lot of text files and each file consists some words. There files can be classified into two categories. You want to visualize a file as a point in a 2D/3D space so that you can see the distribution clearly. So you need to do dimension reduction to transfer a file containing a lot of words into only 2 or 3 dimensions.
The dimensionality of a measurement of something, is the number of numbers required to describe it. So for example the number of numbers needed to describe the location of a point in space will be 3 (x,y and z).
Now lets consider the location of a train along a long but winding track through the mountains. At first glance this may appear to be a 3 dimensional problem, requiring a longitude, latitude and height measurement to specify. But this 3 dimensions can be reduced to one if you just take the distance travelled along the track from the start instead.
If you were given the task of using a neural network or some statistical technique to predict how far a train could get given a certain quantity of fuel, then it will be far easier to work with the 1 dimensional data than the 3 dimensional version.
It's a technique of data mining. Its main benefit is that it allows you to produce a visual representation of many-dimensional data. The human brain is peerless at spotting and analyzing patterns in visual data, but can process a maximum of three dimensions (four if you use time, i.e. animated displays) - so any data with more than 3 dimensions needs to somehow compressed down to 3 (or 2, since plotting data in 3D can often be technically difficult).
BTW, a very simple form of dimensionality reduction is the use of color to represent an additional dimension, for example in heat maps.
Suppose you're building a database of information about a large collection of adult human beings. It's also going to be quite detailed. So we could say that the database is going to have large dimensions.
AAMOF each database record will actually include a measure of the person's IQ and shoe size. Now let's pretend that these two characteristics are quite highly correlated. Compared to IQs shoe sizes may be easy to measure and we want to populate the database with useful data as quickly as possible. One thing we could do would be to forge ahead and record shoe sizes for new database records, postponing the task of collecting IQ data for later. We would still be able to estimate IQs using shoe sizes because the two measures are correlated.
We would be using a very simple form of practical dimension reduction by leaving IQ out of records initially. Principal components analysis, various forms of factor analysis and other methods are extensions of this simple idea.

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