The document analyzes the nutritional status of children and women in the Indian states of Uttar Pradesh and Bihar using TOPSIS and cluster analysis methods. It highlights the critical impact of maternal nutrition on child development and categorizes districts based on multiple nutritional indicators. The findings aim to assess disparities and provide a ranking of districts according to their nutritional performance.

1. NUTRITIONAL STATUS OF CHILDREN AND
INFLUENCING FACTORS IN BIHAR AND UTTAR
PRADESH: DISTRICT WISE ANALYSIS THROUGH
TOPSIS
BY
PROF . C.P.PRAKASAM
FORMER PROFESSOR, IIPS, MUMBAI
prakasamcp60@gmail.com
11/19/2023 NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM 1

2. Nutrition and women and Child Development
Adequate nutrition is critical to child development.
Similarly, malnutrition in women, especially mother, and her weaning practices
influences the growth of child from birth to two years.
A women(mother) with poor nutritional status, has greater risk of obstructed
labour, having baby with low birth weight, producing lower quality of breast
milk, vulnerable to growth retardation of her child.
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3. Objectives
To examine the nutritional status of children under 6 years and women in the
districts of Uttar Pradesh and Bihar.
Classifying the districts of Uttar Pradesh and Bihar according to nutritional
indicators of children and women by applying Cluster Analysis (K-means cluster
method).
Ranking the districts of Uttar Pradesh and Bihar by using Technique for Order
Preference by Similarity to Ideal Solution (TOPSIS) algorithm and discussion.
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4. Data Source and Methodology
District wise Data were derived from NFHS-5 for the states Uttar Pradesh and Bihar
The selected variables are:
V1: Percentage of children below -2sd: Height- for-age (Stunting)
V2: Percentage of children below -2sd: Weight-for-height (wasting)
V3: Percentage of children below -2sd: weight-for-age (underweight)
V4: Percentage of children breastfed within one hour of birth (for children less than 2 years)
V5: Percentage of children under 6 years exclusively breastfed
V6: Percentage of children having any anaemia (11.0 gm)
V7: Percentage of women having any anaemia (<12.0 g/dl)
V8: Percentage of women with BMI <18.5 (Total Thin)
V9: Percentage of women with BMI >=23.0 (Overweight or obese).
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5. Methodology:
I: Cluster Analysis
Cluster analysis is a multivariate data analysis technique to group the
objects (cases) based on a set of user selected characteristics or
attributes
Cluster analysis identify homogenous groups of cases by using
Euclidean distance and it does not make any distinction between
dependent and independent variables. By using Hierarchical
procedure number of clusters identified and later by using K-means
cluster method the means of clusters identified.
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6. II.TOPSIS
II: TOPSIS
By applying Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS) algorithm the
identified clusters, have been ranked to assess
the disparities in the nutritional status of
children and women among the districts in Uttar
Pradesh and Bihar.
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7. TOPSIS METHOD
In this method two artificial alternatives are hypothesized:
Ideal alternative: the one which has the best level for all attributes
considered.
Negative ideal alternative: the one which has the worst attribute
values.
TOPSIS selects the alternative that is the closest to the ideal
solution and farthest from negative ideal alternative.
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8. STEPS INVOLVED
Step 1: Construct normalized decision (data)matrix.
This step transforms various attribute dimensions into non-dimensional
attributes,
which allows comparisons across criteria.
Normalize the data as follows:
rij = xij/ (x2
ij) for i = 1, …, m; j = 1, …, n ……. (1)
i=states, j=time
Step 2: Construct the weighted normalized decision matrix.
Assume we have a set of weights for each criteria wj for j = 1,…n.
Multiply each column of the normalized decision matrix by its associated
weight.
An element of the new matrix is:
vij = wj rij -------------------------------------------------- (2)
Weights have been calculated as suggested by Mohammad Sharif Krimi,et al; (2010);Shannon, C.E. and
Weaver, W (1947)
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NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM

9. WEIGHTS
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NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM
Weights have been
calculated as
suggested by
Mohammad Sharif
Krimi,et al;
(2010);Shannon, C.E.
and Weaver, W (1947)

10. .
Ideal solution
A* = { v1
* , …, vn
*}, where
vj
* ={ max (vij) if j  J ; min (vij) if j  J' }
i i
Negative ideal solution
A' = {v1’, …, vn' }, where
v' = { min (vij) if j  J ; max (vij) if j  J' }
Step 3: Determine the ideal and negative ideal solutions
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NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM
Step 4: Calculate the separation measures for each alternative.
The separation from the ideal alternative is:
Si
* = [  (vj
*– vij)2 ] ½ i = 1, …, m
Similarly, the separation from the negative ideal alternative is:
S'i = [  (vj' – vij)2 ] ½ i = 1, …, m
Step 5: Calculate the relative closeness to the ideal solution Ci
*
Ci
* = S'i / (Si
* +S'i ) , 0  Ci
*  1 ------------------(3)
Select the option with Ci
* closest to 1 is high rank and closest to zero is lowest rank. Hence
lowest rank is given rank “1” close “0” of Ci
* and highest to highest Ci* as highest rank.

11. RESULTS
1.By applying Cluster analysis (K-mean clustering), the districts
have been classified by Nutritional status.
2. By applying TOPSIS method, with in each cluster, the districts
have been ranked.
Analysis have been carried out for Uttar Pradesh, Bihar states
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12. Table: Districts identified according to Nutritional level of Children and Women in
Uttar Pradesh by K-means cluster method
Cluster 1
(18)
Bahraich, Ballia, Balrampur, Banda, Fatehpur, Ghazipur, Gonda, Hamirpur,
Hardoi, Kanauji, Kheri, Mahrajganj, Rae Bareli, Shrawasti, Siddharthnagar,
Sitapur, SK Nagar, Unnao
Cluster2
(17)
Allahabad, Auraiya, Basti, Chitrakoot, Deoria, Jalaun, Jaunpur, Jhansi,
Kushinagar, Lalitpur, Mahoba, Mau, Moradabad, Pilibhit, Saharanpur,
Sonbhadra, Varanasi
Cluster 3
(18)
Amb-Nagar, Amethi, Azamgarh, Baghoat, Bijnor, Bulandshahr, Chandauli,
Faizabad, GB Nagar, Lucknow, Meerut, Mirzapur, Muzaffarnagar, Pratapgarh,
Shamli, SRNagar Bhadhohi, Sultanpur
Cluster 4
(22)
Agra, Alighar,Bara Banki, Bareilly, Budaun, Etah, Etawah, Farrukhabad,
Firozabad, Gorakhpur, Hapur, Jyotiba P nagar, Kanpur Dehat, Kanpur Nagar,
Kanshiram Nagar, Kaushambi, Mahamaya Nagar, Mainpuri, Mathura,
Rampur, Sambhai, Shahjahanpur
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13. Centroid values of Nutritional Status
by cluster in Uttar Pradesh
V1 V2 V3 V4 V5 V6 V7 V8 V9
Cluster1 45.60 18.97 35.63 17.28 60.97 71.72 51.86 24.02 15.23
Cluster2 38.07 21.44 35.82 23.91 58.28 60.43 42.21 18.26 17.91
Cluster3 33.89 14.08 26.89 20.02 62.24 59.80 49.67 17.31 28.15
Cluster4 41.38 16.08 30.87 32.33 58.37 71.64 56.46 17.38 21.83
Total 39.72 17.51 32.18 23.85 59.90 66.28 50.49 19.15 20.87
Table: : Centroid values (Mean) of the nutrition varaibles according to
cluster in Uttar Pradesh
Stunting wasting
underweight anaemia
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14. Uttar Pradesh
45.60
38.07
33.89
41.38
39.72
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V1
35.63 35.82
26.89
30.87
32.18
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V3
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15. Nutrition status in Uttar Pradesh
71.72
60.43 59.80
71.64
66.28
50.00
55.00
60.00
65.00
70.00
75.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V6
17.28
23.91
20.02
32.33
23.85
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V4
60.97
58.28
62.24
58.37
59.90
56.00
57.00
58.00
59.00
60.00
61.00
62.00
63.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V5
15.23
17.91
28.15
21.83 20.87
0.00
5.00
10.00
15.00
20.00
25.00
30.00
Cluster1 Cluster2 Cluster3 Cluster4 Total
V9
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16. Table : : Districts identified according to Nutritional level of
Children and Women in BIHAR by K-means cluster
method
Cluster 1
(9)
Darbhanga, Gopalganj, Madhubani, Muzaffarpur, Pashchim Champaran,
PurbaChamparan, Sheikhpura, Sheohar, Siwan
Cluster 2
(20)
Araria, Aurangabad_ind, Banka, Begusarai. Bhagalpur, Gaya_ind,
Jamui_ind, Kishanganj, Lakhisarai, Madhepura, Munger, Nalanda,
Nawada_ind, Purnia, Rohtas_ind, Saharsa, Samastipur, Sitamarhi, Supaul,
Vaishali
Cluster 3
(9)
Arwal_ind, Bhojpur, Buxar, Jehanabad_ind, Kaimur (Bhabua)ind, Katihar,
Khagaria, Patna, Saran
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17. Centroid values of Nutritional variables
by cluster in Bihar
BIHAR V1 V2 V3 V4 V5 V6 V7 V8 V9
Cluster
Number
Number
of
Districts
Height-for-
age Percent
below -
2sd
Stunting
weight-
for-Height
Percent
below -
2sd
wasting
weight-for-
age Percent
below -
2sd
underweight
Percent
breast feed
within 1
hour of
birth
Percent of
children
under age 6
months
exclusively
breastfed
Percent
children
having
any
anaemia
&lt;11g/dl
Percent
women
having any
anaemia
,12 g/dl
Percent
women
with
BMI&lt;18
.5 (total
thin)
Percent of
women
with BMI
&gt;=25.0
(Over
weight or
obese)
Cluster1 9 42.52 19.74 35.32 29.17 73.62 66.70 58.56 23.20 15.84
Cluster2 20 43.57 23.67 42.88 32.44 58.26 72.98 66.39 27.50 14.48
Cluster 3 9 40.46 28.59 45.58 34.08 38.52 67.00 66.98 24.94 16.41
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18. Nutrition status in BIHAR
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19. ClusterI II III IV
Ci* Ci* Ci* Ci*
1 Rae Bareli 0.335334 1 Basti 0.389468 1 SRNagar_Bhadohi
0.273859 1 Agra 0.272262
2 Hamirpur 0.357391 2 Kushinagar0.397552 2 Pratapgarh 0.308978 2 Kanpur Dehat
0.336602
3 Siddharthnagar
0.393137 3 Jhansi 0.399753 3 Faizabad 0.328515 3 Etawah 0.337087
4 Kheri 0.393306 4 Deoria 0.425930 4 Baghpat 0.335856 4 Rampur 0.373591
5 Gonda 0.415477 5 Mahoba 0.427738 5 Mirzapur 0.349756 5 Mathura 0.386141
6 Sitapur 0.42267 6 Chitrakoot 0.434807 6 Lucknow 0.371380 6 Kanpur Nagar
0.386485
7 Hardoi 0.447003 7 Allahabad 0.470073 7 Bulandshahr
0.423948 7 Firozabad 0.406592
8 Bahraich 0.451184 8 Pilibhit 0.482259 8 Azamgarh 0.425912 8 Hapur 0.418767
9 Ghazipur 0.495239 9 Auraiya 0.485143 9 Meerut 0.428818 9 Shahjahanpur
0.419578
10 SK Nagar 0.512437 10 Moradabad0.524316 10 Muzaffarnagar
0.432077 10 Etah 0.441924
11 Unnao 0.520741 11 Sonbhadra 0.528133 11 Ghaziabad 0.440073 11 Mainpuri 0.446850
12 Shrawasti 0.521376 12 Jaunpur 0.531571 12 Shamli 0.452984 12 Jyotiba P Nagar
0.448543
13 Mahrajganj0.558365 13 Lalitpur 0.575733 13 Bijnor 0.483958 13 Aligarh 0.448936
14 Balrampur 0.561736 14 Varanasi 0.594831 14 Sultanpur 0.484957 14 Bara Banki 0.459707
15 Ballia 0.615392 15 Jalaun 0.614787 15 Amb_ Nagar
0.515459 15 Sambhal 0.461131
16 Fatehpur 0.626403 16 Saharanpur0.652486 16 GB Nagar 0.521783 16 Kaushambi 0.462023
17 Banda 0.637394 17 Mau 0.687880 17 Amethi 0.534890 17 Farrukhabad
0.467191
18 Kannauj 0.655022 18 Chandauli 0.553549 18 Mahamaya Nagar
0.480743
19 Gorakhpur 0.512783
20 Budaun 0.520535
21 Bareilly 0.578332
22 Kanshiram Nagar
0.606729
UTTAR PRADESH: Ci* values for Nutrition NFHS-5 data
Ranking Districts by using TOPSIS algorithm: UTTAR PRADESH
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20. Cluster 1 Ci* Cluster 2 ci* Cluster 3 Ci*
1 Siwan 0.474347 1 Nalanda 0.393119 1 Bhojpur 0.342737
2 Sheohar 0.483221 2 Rohtas_ind0.396679 2 Patna 0.400947
3 Sheikhpura 0.55033 3 Munger 0.421323 3 Katihar 0.483887
4 Muzaffarpur 0.561945 4 Purnia 0.45211 4 Saran 0.501597
5 Pashchim Champaran
0.563116 5 Kishanganj 0.49319 5 Buxar 0.508208
6 Darbhanga 0.578488 6 Bhagalpur 0.51727 6 Arwal_ind 0.57046
7 PurbaChamparan
0.590045 7 Lakhisarai 0.522428 7 Khagaria 0.574502
8 Madhubani 0.612979 8 Vaishali 0.529766 8 Jehanabad_ind
0.582932
9 Gopalganj 0.617255 9 Sitamarhi 0.531255 9 Kaimur (Bhabua)ind
0.708727
10 Aurangabad_ind
0.570562
11 Banka 0.582181
12 Samastipur0.588543
13 Araria 0.593622
14 Begusarai 0.608667
15 Saharsa 0.609959
16 Nawada_ind
0.630704
17 Madhepura0.634035
18 Jamui_ind 0.645699
19 Supaul 0.673151
20 Gaya_ind 0.682067
BIHAR: DISTRICT WISE CI* VALUES FOR NUTRITIONAL STATUS OF CHILDREN AND WOMEN:NFHS-5 DATA
Ranking Districts by using TOPSIS algorithm: BIHAR
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21. Results and Conclusions
With the measurements made according to Height-for-age (Stunting) based on the
youngest living child with mother, 39.7 percent of children in Uttar Pradesh and 42.9
percent in Bihar are Stunting. In cluster 1 45.60 in UP and in Cluster 2 (43.57) in Bihar
found to be more than state average.
66.4 percent of children having any anaemia (11.0 g/dl) in Uttar Pradesh and 69.4
percent in Bihar. In cluster 1 71.72 percent of children anaemia in UP and in cluster 2
(72.98) children anaemia in Bihar which is more than state average.
Brest feeding habits are within one hour found to be less than 30 percent in both states
and around 58 percent of children under age 6 months exclusively breastfed in both
states.
From the above analysis breastfeeding habits shows no influence or less influence in
the nutritional status of children in UP and Bihar.
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22. Conclusions:
Stunting and underweight children are more in the following districts and special
nutritional program for children should be implemented:
Uttar Pradesh:
Bahraich, Ballia, Balrampur, Banda, Fatehpur, Ghazipur, Gonda, Hamirpur,
Hardoi, Kanauji, Kheri, Mahrajganj, Rae Bareli, Shrawasti, Siddharthnagar,
Sitapur, SK Nagar, Unnao
Bihar:
Araria, Aurangabad_ind, Banka, Begusarai. Bhagalpur, Gaya_ind, Jamui_ind,
Kishanganj, Lakhisarai, Madhepura, Munger, Nalanda, Nawada_ind, Purnia,
Rohtas_ind, Saharsa, Samastipur, Sitamarhi, Supaul, Vaishali
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23. According to TOPSIS ranking following districts identified focused districts for special Nutritional programs for children
UTTAR PRADESH
Sitapur
Kheri
Siddharthnagar
Banda
Hardoi
Rae Bareli
Balrampur
BIHAR
Rohtas_ind
Munger
Purnia
Kishanganj
Bhagalpur
Lakhisarai
Vaishali
Sitamarhi
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24. YouTube Links
1.For cluster analysis method : https://youtu.be/watch?v=EDjRPx8Onc8
2. Link to video K_means_cluster_method: https://youtu.be/watch?v=-bYTQvz1tHU
CHANNEL LINK : https://www.youtube.com/@ProfCPPrakasam60
11/19/2023 NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM 24

25. THANKYOU
prakasamcp60@gmail.com
11/19/2023 NUTRITIONAL STATUS-TOPSIS-PROF.C.P.PRAKASAM 25

26. ClusterI II III IV
Ci* Ci* Ci* Ci*
8 Rae Bareli 0.335334 9 Basti 0.389468 17 SRNagar_Bhadohi
0.273859 20 Agra 0.272262
3 Hamirpur 0.357391 12 Kushinagar 0.397552 11 Pratapgarh 0.308978 11 Kanpur Dehat 0.336602
18 Siddharthnagar
0.393137 2 Jhansi 0.399753 5 Faizabad 0.328515 6 Etawah 0.337087
7 Kheri 0.393306 10 Deoria 0.425930 2 Baghpat 0.335856 17 Rampur 0.373591
14 Gonda 0.415477 14 Mahoba 0.427738 16 Mirzapur 0.349756 22 Mathura 0.386141
9 Sitapur 0.42267 1 Chitrakoot 0.434807 8 Lucknow 0.371380 12 Kanpur Nagar 0.386485
4 Hardoi 0.447003 7 Allahabad 0.470073 4 Bulandshahr 0.423948 8 Firozabad 0.406592
10 Bahraich 0.451184 5 Pilibhit 0.482259 1 Azamgarh 0.425912 21 Hapur 0.418767
13 Ghazipur 0.495239 8 Auraiya 0.485143 9 Meerut 0.428818 19 Shahjahanpur 0.419578
16 SK Nagar 0.512437 15 Moradabad 0.524316 10 Muzaffarnagar0.432077 5 Etah 0.441924
6 Unnao 0.520741 17 Sonbhadra 0.528133 7 Ghaziabad 0.440073 16 Mainpuri 0.446850
17 Shrawasti 0.521376 11 Jaunpur 0.531571 18 Shamli 0.452984 10 Jyotiba P Nagar 0.448543
15 Mahrajganj0.558365 13 Lalitpur 0.575733 3 Bijnor 0.483958 1 Aligarh 0.448936
12 Balrampur 0.561736 6 Varanasi 0.594831 12 Sultanpur 0.484957 2 Bara Banki 0.459707
11 Ballia 0.615392 3 Jalaun 0.614787 13 Amb_ Nagar 0.515459 18 Sambhal 0.461131
2 Fatehpur 0.626403 16 Saharanpur 0.652486 6 GB Nagar 0.521783 14 Kaushambi 0.462023
1 Banda 0.637394 4 Mau 0.687880 14 Amethi 0.534890 7 Farrukhabad 0.467191
5 Kannauj 0.655022 15 Chandauli 0.553549 15 Mahamaya Nagar 0.480743
9 Gorakhpur 0.512783
4 Budaun 0.520535
3 Bareilly 0.578332
13 Kanshiram Nagar 0.606729
UTTAR PRADESH: Ci* values for Nutrition NFHS-5 data
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