Systems methods and media for preference clustering are provided. In one example, a clustering system for analyzing a cluster comprises processors and a memory storing instructions that cause the system to calculate a Distance Angular Measure (DAM) for the cluster, the (DAM) comprising a distance component and an angular component of the cluster. In one example, the distance component of the (DAM) includes one of a cluster variation and a cluster radius.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A clustering system for analyzing a cluster, the clustering system comprising: processors; and a memory storing instructions that, when executed by at least one processor among the processors, cause the system to perform operations comprising, at least: calculating a Distance Angular Measure (DAM) for the cluster, the (DAM) comprising a distance component and an angular component of the cluster. 2. The clustering system of claim 1, wherein the distance component of the (DAM) includes one of a cluster variation and a cluster radius. 3. The clustering system of claim 2, wherein the cluster variation is defined by an algorithm comprising: σ C j 2 = ∑ x → ∈ C j   x → - c → j  N C j , where {right arrow over (c)}j is a center of the cluster Cj,{right arrow over (x)}εCj and NCj is a number of observations or points in Cj. 4. The clustering system of claim 2, wherein the cluster radius is defined by an algorithm comprising: φCj=max{right arrow over (x)}εCjd({right arrow over (x)},{right arrow over (c)}j) 5. The clustering system of claim 4, wherein a distance between two points in the cluster is defined by an algorithm comprising: ρ({right arrow over (x)},{right arrow over (y)})=√{square root over (∥{right arrow over (x)}∥+∥{right arrow over (y)}∥)} 1. 6. The clustering system of claim 1, wherein the angular component of the (DAM) includes a cosine function. 7. A method for analyzing a cluster, the method comprising: calculating a Distance Angular Measure (DAM) for the cluster, the (DAM) comprising a distance component and an angular component of the cluster. 8. The method of claim 7, wherein the distance component of the (DAM) includes one of a cluster variation and a cluster radius. 9. The method of claim 8, further comprising defining the cluster variation by an algorithm comprising: σ C j 2 = ∑ x → ∈ C j   x → - c → j  N C j , where {right arrow over (c)}j is a center of the cluster Cj,{right arrow over (x)}εCj and NCj is a number of observations or points in Cj. 10. The method of claim 8, further comprising defining the cluster radius by an algorithm comprising: φCj=max{right arrow over (x)}εCjd({right arrow over (x)},{right arrow over (c)}j) 11. The method of claim 10, further comprising defining a distance between two points in the duster by an algorithm comprising: φ({right arrow over (x)},{right arrow over (y)})=√{square root over (∥{right arrow over (x)}∥+∥{right arrow over (y)}∥)} 1. 12. The method of claim 7, further comprising including a cosine function into the angular component of the (DAM) 13. A machine-readable medium carrying instructions which, when read by a machine, cause the machine to perform operations comprising, at least: calculating a Distance Angular Measure (DAM) for the cluster, the (DAM) comprising a distance component and an angular component of the cluster. 14. The medium of claim 13, wherein the distance component of the (DAM) includes one of a cluster variation and a cluster radius. 15. The medium of claim 14, wherein the cluster variation is defined by an algorithm comprising: σ C j 2 = ∑ x → ∈ C j   x → - c → j  N C j , where {right arrow over (c)}j is a center of the cluster Cj,{right arrow over (x)}εCj and NCj is a number of observations or points in Cj. 16. The medium of claim 14, wherein the cluster radius is defined by an algorithm comprising: φCj=max{right arrow over (x)}εCjd({right arrow over (x)},{right arrow over (c)}j) 17. The medium of claim 16, wherein a distance between two points in the cluster is defined by an algorithm comprising: φ({right arrow over (x)},{right arrow over (y)})=√{square root over (∥{right arrow over (x)}∥+∥{right arrow over (y)}∥)} 1. 18. The medium of claim 13, wherein the angular component of the (DAM) includes a cosine function.