# US 7,412,429 B1 · Method for data classification by kernel density shape interpolation of clusters

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- Number: US 7,412,429 B1
- Document ID: US7412429B1
- Status: Granted
- Kind: B1
- Application number: 11/940,739
- Filed: 2007-11-15
- Granted: 2008-08-12
- Earliest claimed: 2007-11-15
- Assignees: International Business Machines Corporation
- Inventors: Tanveer Syeda-Mahmood; Peter J. Haas; John M. Lake; Guy M. Lohman
- Web page: https://patentgrep.com/patent/US7412429B1

## CPC

- G06N 20/00: Machine learning
- G06F 18/2321: using statistics or function optimisation, e.g. modelling of probability density functions
- G06F 18/2414: {Smoothing the distance, e.g. radial basis function networks [RBFN]}
- G06N 20/10: using kernel methods, e.g. support vector machines [SVM]
- G06V 10/764: using classification, e.g. of video objects
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING

## Abstract

A method for obtaining a shape interpolated representation of shapes of one or more clusters in an image of a dataset that has been clustered comprises generating a density estimate value of each grid point of a set of grid points sampled from the image at a specified resolution for each cluster in the image using a kernel density function; evaluating the density estimate value of each grid point for each cluster to identify a maximum density estimate value of each grid point and a cluster associated with the maximum density estimate value of each grid point; and adding each grid point for which the maximum density estimate value exceeds a specified threshold to the cluster associated with the maximum density estimate value for the grid point to form a shape interpolated representation of the one or more clusters.

## Claims

### Claim 1

A method executed on a computer for obtaining a shape interpolated representation of shapes of one or more clusters in an image of a dataset that has been clustered, the method comprising:
generating a density estimate value of each grid point of a set of grid points sampled from the image at a specified resolution for each cluster in the image using a kernel density function;
evaluating the density estimate value of each grid point for each cluster to identify a maximum density estimate value of each grid point and a cluster associated with the maximum density estimate value of each grid point; and
adding each grid point for which the maximum density estimate value exceeds a specified threshold to the cluster associated with the maximum density estimate value for the grid point to form a shape interpolated representation of the one or more clusters.

### Claim 2 (depends on 1)

The method of claim 1, wherein the dataset has been clustered using a two-stage clustering method, the two-stage clustering method comprising:
clustering the dataset using an unsupervised, non-parametric clustering method to generate a set of cluster shapes each comprising a set of data points of the dataset; and
clustering the data points of each cluster shape of the set of cluster shapes using a supervised, partitional clustering method to partition each cluster shape into a specified number of cluster regions.

### Claim 3 (depends on 1)

The method of claim 1, wherein the kernel density function is a Gaussian kernel.

### Claim 4 (depends on 1)

The method of claim 1, further comprising merging any spatially adjacent clusters in the shape interpolated representation and removing any spatially disjointed clusters in the shape interpolated representation.

### Claim 5 (depends on 1)

The method of claim 1, further comprising classifying a new data point by performing a method comprising:
generating a density estimate value of the new data point for each cluster in the image using the kernel density function;
evaluating the density estimate value of the new data point for each cluster to identify a maximum density estimate value of the new data point and a cluster associated with the maximum density estimate value; and
adding the new data point to the cluster associated with the maximum density estimate value in the shape interpolated representation if the maximum density estimate value exceeds a specified threshold to classify the new data point.