MDS statistics

Movie BioloMICS: Multi Dimensional Scaling, from 3.38 min.

When running a Multi-Dimensional Scaling analysis, the software produces a 3D visualization and a text file containing the information related to the eigenvalues and eigenvectors.

To visualize this, under Home, click Show statistics.

An example is given below:

Eigenvalues

Dimensions	Eigenvalue	Percent	Scree plot	Cumulative pct.

1	0.4292	40.2	....................	40.2
2	0.1733	16.2	....................	56.4
3	0.0969	9.1	....................	65.5
4	0.0650	6.1	....................	71.5
5	0.0387	3.6	....................	75.2
6	0.0207	1.9	....................	77.1
7	0.0097	0.9	....................	78.0
8	0.0045	0.4	....................	78.4
9	0.0024	0.2	....................	78.7
10	0.0000	0.0	....................	78.7
11	-0.0008	0.1	....................	78.7
12	-0.0014	0.1	....................	78.9
13	-0.0040	0.4	....................	79.2
14	-0.0090	0.8	....................	80.1
15	-0.0125	1.2	....................	81.3
16	-0.0263	2.5	....................	83.7
17	-0.1740	16.3	....................	100.0

Fit

Dimensions	Stress	*GOF estimate()**

1	0.3948	poor
2	0.2921	poor
3	0.2362	poor
4	0.2459	poor
5	0.2478	poor
6	0.2544	poor
7	0.2584	poor
8	0.2615	poor
9	0.2628	poor
10	0.2628	poor

Number of dissimilarities: 136

Mean of dissimilarities: 0.2441

Sum of Squared Dissimilarities: 2.3103

(*) Goodness-of-Fit estimate: Kruskal (1964) advise about stress values based on his experience. Some authors caution against using a table like this since acceptable values of stress depends on the quality of the distance matrix and the number of objects in that matrix.

Solution (using 10 dimensions)

Variable - record	Dim(1)	Dim(2)	Dim(3)	Dim(4)	Dim(5)	Dim(6)	Dim(7)	Dim(8)	Dim(9)	Dim(10)

0. CBS 14	0.4219	-0.1455	0.0311	-0.0787	-0.0012	-0.0117	-0.0045	-0.0025	0.0033	0.0000
1. CBS 17	0.1810	-0.0253	-0.0630	0.1117	0.0452	-0.0540	0.0116	0.0084	-0.0155	0.0000
2. CBS 20	0.1678	-0.0372	-0.0001	0.1024	-0.0233	0.0369	-0.0164	0.0163	0.0189	0.0000
3. CBS 52	-0.1097	-0.0743	-0.0268	-0.0853	-0.0680	-0.0763	0.0110	0.0249	0.0016	0.0000
4. CBS 53	-0.1873	-0.0176	-0.0540	-0.0004	-0.0664	0.0165	0.0386	0.0003	-0.0073	0.0000
5. CBS 54	-0.3062	-0.1589	-0.0029	0.0924	0.0196	0.0075	-0.0049	-0.0056	0.0026	0.0000
6. CBS 71	0.0772	-0.0912	-0.1590	0.0224	0.0006	0.0336	0.0054	-0.0182	-0.0030	0.0000
7. CBS 72	-0.0731	0.0544	0.0641	0.0222	0.0633	-0.0328	-0.0102	0.0044	-0.0112	0.0000
8. CBS 73	-0.0261	0.0506	0.1230	0.0356	0.0213	0.0101	0.0147	0.0304	0.0091	0.0000
9. CBS 74	-0.0045	0.0242	0.0588	-0.0006	-0.0270	-0.0162	0.0378	-0.0289	0.0154	0.0000
10. CBS 75	-0.0530	0.0582	0.0759	-0.0147	0.0429	-0.0004	-0.0114	-0.0176	0.0015	0.0000
11. CBS 76	0.0345	0.0109	0.0841	-0.0112	-0.0408	0.0191	-0.0179	-0.0108	-0.0327	0.0000
12. CBS 77	0.0006	-0.0162	0.0615	-0.0435	-0.0380	0.0733	0.0005	0.0133	-0.0056	0.0000
13. CBS 78	-0.0179	0.0049	0.0521	-0.0312	0.0299	-0.0178	0.0043	-0.0250	0.0108	0.0000
14. CBS 79	-0.1049	0.0574	-0.0560	-0.0102	-0.0514	-0.0232	-0.0722	-0.0044	0.0091	0.0000
15. CBS 82	-0.1050	-0.0065	-0.0988	-0.1198	0.1125	0.0308	0.0003	0.0133	0.0019	0.0000
16. CBS 94	0.1047	0.3122	-0.0901	0.0089	-0.0191	0.0047	0.0132	0.0016	0.0010	0.0000

Note: Solution based on 10 dimensions.

Dissimilarities

Pair	Actual diss.	Pred. diss.	Difference	Difference pct.

(0,1)	0.1904	0.3497	-0.1594	-83.7
(0,2)	0.1215	0.3372	-0.2156	-177.5
(0,3)	0.4805	0.5484	-0.0680	-14.2
(0,4)	0.6124	0.6387	-0.0263	-4.3
(0,5)	0.7468	0.7494	-0.0026	-0.3
(0,6)	0.2914	0.4131	-0.1216	-41.7
(0,7)	0.5291	0.5488	-0.0197	-3.7
(0,8)	0.4788	0.5131	-0.0343	-7.2
(0,9)	0.3889	0.4700	-0.0811	-20.9
(0,10)	0.4738	0.5249	-0.0512	-10.8
(0,11)	0.3644	0.4313	-0.0669	-18.4
(0,12)	0.3952	0.4532	-0.0579	-14.7
(0,13)	0.4066	0.4695	-0.0629	-15.5
(0,14)	0.5371	0.5816	-0.0445	-8.3
(0,15)	0.5091	0.5749	-0.0659	-12.9
(0,16)	0.5497	0.5775	-0.0278	-5.1
(1,2)	0.1185	0.1391	-0.0206	-17.4
(1,3)	0.3613	0.3754	-0.0141	-3.9
(1,4)	0.3810	0.4082	-0.0273	-7.2
(1,5)	0.4000	0.5142	-0.1142	-28.6
(1,6)	0.1300	0.2070	-0.0770	-59.2
(1,7)	0.2708	0.3105	-0.0397	-14.7
(1,8)	0.2789	0.3080	-0.0291	-10.4
(1,9)	0.2644	0.2720	-0.0077	-2.9
(1,10)	0.2626	0.3184	-0.0558	-21.3
(1,11)	0.2619	0.2717	-0.0097	-3.7
(1,12)	0.2592	0.3092	-0.0500	-19.3
(1,13)	0.2615	0.2785	-0.0170	-6.5
(1,14)	0.3432	0.3487	-0.0054	-1.6
(1,15)	0.3863	0.3862	0.0000	0.0
(1,16)	0.2477	0.3727	-0.1250	-50.5
(2,3)	0.3752	0.3610	0.0142	3.8
(2,4)	0.3462	0.3824	-0.0362	-10.5
(2,5)	0.3467	0.4932	-0.1465	-42.3
(2,6)	0.1767	0.2133	-0.0366	-20.7
(2,7)	0.2619	0.3007	-0.0389	-14.8
(2,8)	0.2140	0.2625	-0.0485	-22.6
(2,9)	0.2492	0.2353	0.0139	5.6
(2,10)	0.2077	0.2909	-0.0832	-40.1
(2,11)	0.2092	0.2100	-0.0008	-0.4
(2,12)	0.2144	0.2365	-0.0221	-10.3
(2,13)	0.2541	0.2547	-0.0006	-0.2
(2,14)	0.3020	0.3274	-0.0253	-8.4
(2,15)	0.3658	0.3919	-0.0260	-7.1
(2,16)	0.2845	0.3812	-0.0968	-34.0
(3,4)	0.0197	0.1651	-0.1453	-736.4
(3,5)	0.0720	0.3062	-0.2342	-325.3
(3,6)	0.2363	0.2881	-0.0518	-21.9
(3,7)	0.2161	0.2406	-0.0245	-11.3
(3,8)	0.2546	0.2743	-0.0197	-7.7
(3,9)	0.1914	0.2107	-0.0193	-10.1
(3,10)	0.2234	0.2381	-0.0147	-6.6
(3,11)	0.2329	0.2429	-0.0100	-4.3
(3,12)	0.2051	0.2206	-0.0155	-7.5
(3,13)	0.1867	0.1987	-0.0120	-6.4
(3,14)	0.1564	0.1865	-0.0301	-19.3
(3,15)	0.1992	0.2351	-0.0359	-18.0
(3,16)	0.3964	0.4666	-0.0702	-17.7
(4,5)	0.0484	0.2341	-0.1857	-383.8
(4,6)	0.2109	0.3053	-0.0943	-44.7
(4,7)	0.2081	0.2331	-0.0251	-12.1
(4,8)	0.2297	0.2697	-0.0400	-17.4
(4,9)	0.1611	0.2278	-0.0667	-41.4
(4,10)	0.2081	0.2366	-0.0286	-13.7
(4,11)	0.2349	0.2717	-0.0368	-15.7
(4,12)	0.1946	0.2370	-0.0423	-21.7
(4,13)	0.1918	0.2324	-0.0406	-21.2
(4,14)	0.1333	0.1640	-0.0307	-23.0
(4,15)	0.2080	0.2389	-0.0309	-14.9
(4,16)	0.4104	0.4456	-0.0352	-8.6
(5,6)	0.2406	0.4269	-0.1862	-77.4
(5,7)	0.2339	0.3363	-0.1024	-43.8
(5,8)	0.2764	0.3784	-0.1019	-36.9
(5,9)	0.2162	0.3772	-0.1610	-74.5
(5,10)	0.2339	0.3602	-0.1263	-54.0
(5,11)	0.2906	0.4104	-0.1198	-41.2
(5,12)	0.2636	0.3810	-0.1174	-44.5
(5,13)	0.2063	0.3599	-0.1536	-74.4
(5,14)	0.2128	0.3335	-0.1207	-56.7
(5,15)	0.2256	0.3571	-0.1315	-58.3
(5,16)	0.6340	0.6382	-0.0041	-0.7
(6,7)	0.2591	0.3205	-0.0614	-23.7
(6,8)	0.2880	0.3378	-0.0498	-17.3
(6,9)	0.2402	0.2697	-0.0294	-12.3
(6,10)	0.2537	0.3148	-0.0611	-24.1
(6,11)	0.2268	0.2755	-0.0486	-21.4
(6,12)	0.1957	0.2618	-0.0661	-33.8
(6,13)	0.1856	0.2636	-0.0780	-42.0
(6,14)	0.2333	0.2814	-0.0481	-20.6
(6,15)	0.1825	0.2789	-0.0964	-52.8
(6,16)	0.3338	0.4124	-0.0786	-23.5
(7,8)	0.0666	0.1057	-0.0392	-58.9
(7,9)	0.0379	0.1368	-0.0989	-260.7
(7,10)	0.0173	0.0635	-0.0461	-266.0
(7,11)	0.1386	0.1710	-0.0324	-23.4
(7,12)	0.1613	0.1910	-0.0296	-18.4
(7,13)	0.0178	0.1067	-0.0889	-497.9
(7,14)	0.1640	0.1846	-0.0206	-12.6
(7,15)	0.2157	0.2414	-0.0257	-11.9
(7,16)	0.3254	0.3619	-0.0365	-11.2
(8,9)	0.0422	0.1171	-0.0750	-177.9
(8,10)	0.0276	0.0957	-0.0681	-246.6
(8,11)	0.0950	0.1320	-0.0370	-38.9
(8,12)	0.1121	0.1532	-0.0411	-36.7
(8,13)	0.0532	0.1252	-0.0720	-135.2
(8,14)	0.2266	0.2357	-0.0091	-4.0
(8,15)	0.2868	0.3036	-0.0167	-5.8
(8,16)	0.3275	0.3664	-0.0389	-11.9
(9,10)	0.0311	0.1091	-0.0780	-250.9
(9,11)	0.0802	0.0981	-0.0180	-22.4
(9,12)	0.0997	0.1235	-0.0237	-23.8
(9,13)	0.0130	0.0770	-0.0640	-492.7
(9,14)	0.1841	0.1945	-0.0105	-5.7
(9,15)	0.2720	0.2741	-0.0021	-0.8
(9,16)	0.2310	0.3456	-0.1146	-49.6
(10,11)	0.1090	0.1364	-0.0274	-25.1
(10,12)	0.1278	0.1502	-0.0225	-17.6
(10,13)	0.0219	0.0760	-0.0542	-247.8
(10,14)	0.1695	0.1829	-0.0135	-7.9
(10,15)	0.2182	0.2353	-0.0171	-7.9
(10,16)	0.3028	0.3498	-0.0471	-15.5
(11,12)	0.0544	0.0897	-0.0353	-64.8
(11,13)	0.1035	0.1147	-0.0111	-10.8
(11,14)	0.2069	0.2188	-0.0119	-5.7
(11,15)	0.2983	0.3012	-0.0030	-1.0
(11,16)	0.3018	0.3597	-0.0579	-19.2
(12,13)	0.1087	0.1252	-0.0166	-15.2
(12,14)	0.2081	0.2162	-0.0081	-3.9
(12,15)	0.2518	0.2593	-0.0076	-3.0
(12,16)	0.3409	0.3871	-0.0462	-13.5
(13,14)	0.1739	0.1881	-0.0142	-8.1
(13,15)	0.1968	0.2216	-0.0247	-12.6
(13,16)	0.2928	0.3675	-0.0747	-25.5
(14,15)	0.2252	0.2309	-0.0058	-2.6
(14,16)	0.2849	0.3458	-0.0610	-21.4
(15,16)	0.3530	0.4249	-0.0719	-20.4

Note: Predicted values for 10 dimensions.

Note on Eigenvalues from Wikipedia:

“Linear transformations of space—such as rotation, reflection, stretching, compression, shear or any combination of these—may be visualized by the effect they produce on vectors. Vectors can be visualized as arrows pointing from one point to another.

An eigenvector of a linear transformation is a vector that is either left unaffected or simply multiplied by a scale factor after the transformation (the former corresponds to a scale factor of 1).

The eigenvalue of a non-zero eigenvector is the scale factor by which it has been multiplied.

An eigenvalue of a linear transformation is a factor for which it has a non-zero eigenvector with that factor as its eigenvalue.

The eigenspace corresponding to a given eigenvalue of a linear transformation is the vector space of all eigenvectors with that eigenvalue.

The geometric multiplicity of an eigenvalue is the dimension of the associated eigenspace.

The spectrum of a transformation on a finite dimensional vector space is the set of all its eigenvalues. (In the infinite-dimensional case, the concept of spectrum is more subtle and depends on the topology on the vector space.)

For instance, an eigenvector of a rotation in three dimensions is a vector located within the axis about which the rotation is performed. The corresponding eigenvalue is 1 and the corresponding eigenspace contains all the vectors along the axis. As this is a one-dimensional space, its geometric multiplicity is one. This is the only eigenvalue of the spectrum (of this rotation) that is a real number”.

A three dimensional representation of the results is produced (see 3D view window above) and important options can be cited: zoom in and out, access to several options allowing to change the coloring and the visibility of the displayed items, enable/disable rotation around the X, Y, Z axis when holding the left button of the mouse and moving it on the graphic, show/hide labels of items, change coloring of labels, change size of labels, change format/size/diameter of items, show/hide coloring of side panels and axes, copy 3D graphic to clipboard, print 3D graphic to default printer, etc.

Click on Select fields, and choose the fields to be displayed in the main results grid. Select the fields from the left list and add them to the right grid using the arrow button. The arrow button pointing to the left removes characters from Selected fields, up and down arrows shift the order of displayed characters. Click on Save and close (

) to go back to 3D visualization.